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Determine the solutions to the quadratic equation -4x^2 – 32x – 64 = 0.?
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Quadratic Equation Questions with Solutions – Quadratic Equation Questions: We all have studied the quadratic equation in our post-metrics syllabus of Algebra, as it constitutes an important The quadratic equation can be basically of two types which are the quadratic equation and the linear equation. In the given equation Ax² +bx+c=0…This page will show you how to use the quadratic formula to get the two roots of a quadratic equation. Fill in the boxes to the right, then click the button to see how it's done. It is most commonly note that a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant term (the…Determine if a quadratic equation has real or non-real solutions by finding the value of the discriminant. So let's do an example, solving a quadratic equation that will have no real solution. So if I were to solve the quadratic equation "0 is equal to 2x squared minus 4x plus 4," I know first…
Solve a Quadratic Equation Using the Quadratic Formula – WebMath – Hence the solution to the quadratic equation is.Find the Quadratic Equation Given the Roots. are the two real distinct solutions for the quadratic equation, which means that.MATHS. Quadratic Equations. Answer. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Quadratic Equations with No Real Solution Tutorial | Sophia Learning – OrethaWilkison OrethaWilkison. Answer: Option 3rd is correct. x = -4 and x = 4. Step-by-step explanation: Given the equation Take square root both sides we have; Simplify: Therefore, the solution for the given equation are: x = -4 and x = 4.Algebra Quadratic Equations and Functions Quadratic Formula. #(0+-sqrt(-64))/(2)#. The number under the square root is negative, so there are no real solutions. Finding the imaginary solutions (#i=sqrt(-1)#)Quadratic Equation Solver. What do you want to calculate? Quadratic equations have an x^2 term, and can be rewritten to have the form: a x 2 + b x + c = 0.
Convert to a hyperbola to standard form to find foci, vertices, center and asymptotes – .
Solve a Quadratic Eqaution Using Square Roots x^2+8x=2(32+4x) – We're asked to solve the given equation.
The first step is to
simplify the right side by clearing the parentheses. To clear the parentheses,
we distribute two. This gives us the equation
x squared plus eight x equals two times 32 is 64, plus two times four x is eight x. Notice how we have an eight x term on both sides of the equation. So if we subtract eight x on
both sides as the next step, notice how we have eight x
minus eight x on both sides, which simplifies to zero here and here. And the equation simplifies nicely to x squared equals 64. So because there's no longer an x term, we can actually solve
this quadratic equation using the square root
property shown here below where if x squared is equal to c, then x is equal to plus or minus c. So we take the square root of
both sides of the equation, but to make sure we get both solutions, we do include a plus or minus on the right side of the equation. So going back to our equation, to solve for x, we undo the squaring by taking the square root of
both sides of the equation. We include a plus or minus on the right. The square root of x squared
is equal to one factor of x. We have x equals plus or
minus the square root of 64. Because 64 is equal to eight
times eight or eight squared, the square root of 64 is equal to eight. This gives us our solutions
of x equals negative eight or x equals positive eight. I do want to make one more comment about this plus or minus here. If we go back to the
equation x squared equals 64 and we take the square root of both sides, what's really happening
here is that the square root of x squared must be positive, and therefore the square
root of x squared is equal to the absolute value of x. And then on the right side, the square root of 64 is equal to eight. And because we have the absolute
value of x equals eight, we know x can equal
positive or negative eight because when we take the absolute value, we will get positive eight. But including the plus or
minus here is often explained in textbooks as we see here below. Either way, make sure we have
a plus or minus on the right so that we get both solutions. I also want to make another
point about the equation in the form x squared equals 64. Instead of using the square root property, we could have also just set
the equation equal to zero and solve by factoring. If we subtract 64 on both sides, we get the equation x
squared minus 64 equals zero. And notice x squared minus 64
is a difference of squares, which factors into the
quantity x plus eight times the quantity x minus eight, and then this product is equal to zero when x plus eight equals zero or when x minus eight equals zero. Solving for x, we do get
x equals negative eight or x equals positive eight. But notice how when we
don't have an x term, using the square root property
is a very efficient way of solving this type of equation. And now before we go, let's verify these solutions actually work by substituting negative
eight and positive eight for x back into the original equation. So let's first check x
equals negative eight. Substituting negative eight for x, we have the square of negative eight, plus eight times negative eight equals two times the quantity 32, plus four times negative eight. Simplifying, the square
of negative eight is 64, plus eight times negative
eight is negative 64. On the right, we have two
times the quantity 32, plus four times negative
eight is negative 32. Continuing to simplify, on the
left we're adding opposites. The sum is zero equals on
the right we have two times, here we have opposites, and
therefore the sum is also zero. Two times zero is zero. Zero equals zero is true, verifying the solution of
x equals negative eight. Now let's check x equals positive eight. Substituting positive eight for x, we have the square of eight, plus eight times eight equals
two times the quantity 32, plus four times eight. Simplifying, eight squared is 64, plus eight times eight is also 64, equals on the right we have
two times the quantity 32, plus four times eight is 32. 64 plus 64 is 128, equals two times the
quantity 32 plus 32 is 64, and two times 64 is 128, verifying x equals eight
is also a solution. I hope you found this helpful. .
Solving a quadratic equation by factoring using AC method – .