Question Find the solution to the quadratic equation $x^{2} = 8x + 9$ by completing the square.

Studdy Solution

STEP 1

Assumptions
1. We are given the quadratic equation $x^{2} = 8x + 9$ .
2. We need to complete the square to solve the equation.
3. Completing the square involves creating a perfect square trinomial on one side of the equation.

STEP 2

First, we rewrite the equation by moving the linear term to the left side.
$x^{2} - 8x = 9$

STEP 3

To complete the square, we need to add a specific value to both sides of the equation to form a perfect square trinomial on the left side. The value to add is the square of half the coefficient of $x$ .

STEP 4

Calculate half the coefficient of $x$ .
$\frac{1}{2} \times -8 = -4$

STEP 5

Square the result from the previous step to find the value to add to both sides of the equation.
$(-4)^2 = 16$

STEP 6

Add 16 to each side of the equation to complete the square.
$x^{2} - 8x + 16 = 9 + 16$

STEP 7

Now the left side of the equation is a perfect square trinomial, and the right side is the sum of 9 and 16.
$x^{2} - 8x + 16 = 25$
The next step to complete the square is to add 16 to each side.

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Question Find the solution to the quadratic equation $x^{2} = 8x + 9$ by completing the square.

Studdy Solution

STEP 1

Assumptions
1. We are given the quadratic equation $x^{2} = 8x + 9$ .
2. We need to complete the square to solve the equation.
3. Completing the square involves creating a perfect square trinomial on one side of the equation.

STEP 2

First, we rewrite the equation by moving the linear term to the left side.
$x^{2} - 8x = 9$

STEP 3

To complete the square, we need to add a specific value to both sides of the equation to form a perfect square trinomial on the left side. The value to add is the square of half the coefficient of $x$ .

STEP 4

Calculate half the coefficient of $x$ .
$\frac{1}{2} \times -8 = -4$

STEP 5

Square the result from the previous step to find the value to add to both sides of the equation.
$(-4)^2 = 16$

STEP 6

Add 16 to each side of the equation to complete the square.
$x^{2} - 8x + 16 = 9 + 16$

STEP 7

Now the left side of the equation is a perfect square trinomial, and the right side is the sum of 9 and 16.
$x^{2} - 8x + 16 = 25$
The next step to complete the square is to add 16 to each side.

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Question Find the solution to the quadratic equation x2=8x+9x^{2} = 8x + 9x2=8x+9 by completing the square.

Studdy Solution

STEP 1

Assumptions1. We are given the quadratic equation x2=8x+9x^{2} = 8x + 9x2=8x+9.2. We need to complete the square to solve the equation.3. Completing the square involves creating a perfect square trinomial on one side of the equation.

STEP 2

First, we rewrite the equation by moving the linear term to the left side.x2−8x=9x^{2} - 8x = 9x2−8x=9

STEP 3

To complete the square, we need to add a specific value to both sides of the equation to form a perfect square trinomial on the left side. The value to add is the square of half the coefficient of xxx.

STEP 4

Calculate half the coefficient of xxx.12×−8=−4\frac{1}{2} \times -8 = -421​×−8=−4

STEP 5

Square the result from the previous step to find the value to add to both sides of the equation.(−4)2=16(-4)^2 = 16(−4)2=16

STEP 6

Add 16 to each side of the equation to complete the square.x2−8x+16=9+16x^{2} - 8x + 16 = 9 + 16x2−8x+16=9+16

STEP 7

Now the left side of the equation is a perfect square trinomial, and the right side is the sum of 9 and 16.x2−8x+16=25x^{2} - 8x + 16 = 25x2−8x+16=25The next step to complete the square is to add 16 to each side.

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Studdy solves anything!

Start learning now

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

Question Find the solution to the quadratic equation $x^{2} = 8x + 9$ by completing the square.

Assumptions
1. We are given the quadratic equation $x^{2} = 8x + 9$ .
2. We need to complete the square to solve the equation.
3. Completing the square involves creating a perfect square trinomial on one side of the equation.

First, we rewrite the equation by moving the linear term to the left side.
$x^{2} - 8x = 9$

To complete the square, we need to add a specific value to both sides of the equation to form a perfect square trinomial on the left side. The value to add is the square of half the coefficient of $x$ .

Calculate half the coefficient of $x$ .
$\frac{1}{2} \times -8 = -4$

Square the result from the previous step to find the value to add to both sides of the equation.
$(-4)^2 = 16$

Add 16 to each side of the equation to complete the square.
$x^{2} - 8x + 16 = 9 + 16$

Now the left side of the equation is a perfect square trinomial, and the right side is the sum of 9 and 16.
$x^{2} - 8x + 16 = 25$
The next step to complete the square is to add 16 to each side.