Solved on Sep 28, 2023

Solve the quadratic equation $4x(x-4)=24$ by completing the square.

STEP 1

Assumptions1. We are given the equation $4x(x-4) =24$ . . We are asked to complete the square.

STEP 2

First, we need to rewrite the equation in the standard form of a quadratic equation, which is $ax^2 + bx + c =0$ .
$4x^2 -16x =24$

STEP 3

Next, we need to isolate the terms with $x$ on one side of the equation.
$x^2 -16x -24 =0$

STEP 4

We can simplify the equation by dividing all terms by4.
$x^2 -4x -6 =0$

STEP 5

To complete the square, we need to add the square of half the coefficient of $x$ to both sides of the equation. The coefficient of $x$ is -4, so half of this is -2, and the square of -2 is4.
$x^2 -4x +4 = +4$

STEP 6

Now, the left side of the equation is a perfect square, and we can simplify the right side.
$(x -2)^2 =10$ We have now completed the square.

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Solve the quadratic equation $4x(x-4)=24$ by completing the square.

STEP 1

Assumptions1. We are given the equation $4x(x-4) =24$ . . We are asked to complete the square.

STEP 2

First, we need to rewrite the equation in the standard form of a quadratic equation, which is $ax^2 + bx + c =0$ .
$4x^2 -16x =24$

STEP 3

Next, we need to isolate the terms with $x$ on one side of the equation.
$x^2 -16x -24 =0$

STEP 4

We can simplify the equation by dividing all terms by4.
$x^2 -4x -6 =0$

STEP 5

To complete the square, we need to add the square of half the coefficient of $x$ to both sides of the equation. The coefficient of $x$ is -4, so half of this is -2, and the square of -2 is4.
$x^2 -4x +4 = +4$

STEP 6

Now, the left side of the equation is a perfect square, and we can simplify the right side.
$(x -2)^2 =10$ We have now completed the square.

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Solve the quadratic equation 4x(x−4)=244x(x-4)=244x(x−4)=24 by completing the square.

STEP 1

Assumptions1. We are given the equation 4x(x−4)=244x(x-4) =244x(x−4)=24. . We are asked to complete the square.

STEP 2

First, we need to rewrite the equation in the standard form of a quadratic equation, which is ax2+bx+c=0ax^2 + bx + c =0ax2+bx+c=0.4x2−16x=244x^2 -16x =244x2−16x=24

STEP 3

Next, we need to isolate the terms with xxx on one side of the equation.x2−16x−24=0x^2 -16x -24 =0x2−16x−24=0

STEP 4

We can simplify the equation by dividing all terms by4.x2−4x−6=0x^2 -4x -6 =0x2−4x−6=0

STEP 5

To complete the square, we need to add the square of half the coefficient of xxx to both sides of the equation. The coefficient of xxx is -4, so half of this is -2, and the square of -2 is4.x2−4x+4=+4x^2 -4x +4 = +4x2−4x+4=+4

STEP 6

Now, the left side of the equation is a perfect square, and we can simplify the right side.(x−2)2=10(x -2)^2 =10(x−2)2=10We have now completed the square.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the quadratic equation $4x(x-4)=24$ by completing the square.

Assumptions1. We are given the equation $4x(x-4) =24$ . . We are asked to complete the square.

First, we need to rewrite the equation in the standard form of a quadratic equation, which is $ax^2 + bx + c =0$ .
$4x^2 -16x =24$

Next, we need to isolate the terms with $x$ on one side of the equation.
$x^2 -16x -24 =0$

We can simplify the equation by dividing all terms by4.
$x^2 -4x -6 =0$

To complete the square, we need to add the square of half the coefficient of $x$ to both sides of the equation. The coefficient of $x$ is -4, so half of this is -2, and the square of -2 is4.
$x^2 -4x +4 = +4$

Now, the left side of the equation is a perfect square, and we can simplify the right side.
$(x -2)^2 =10$ We have now completed the square.