Question
Completing the Square & the Quadratic Formula Practice
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Question
Complete the square to identify the two values that solve the following quadratic equation: x2+8x=9
.(1 point)
x=
Remaining Attempts : 3
Answers
GPT-4o mini
To solve the quadratic equation \(x^2 + 8x = 9\) by completing the square, we will follow these steps:
1. Move the constant to the right side of the equation:
\[
x^2 + 8x - 9 = 0
\]
2. Rearrange it:
\[
x^2 + 8x = 9
\]
3. To complete the square, take half of the coefficient of \(x\) (which is 8), square it, and add that value to both sides. Half of 8 is 4, and squaring it gives 16:
\[
x^2 + 8x + 16 = 9 + 16
\]
\[
x^2 + 8x + 16 = 25
\]
4. Now, the left side factors as:
\[
(x + 4)^2 = 25
\]
5. Take the square root of both sides:
\[
x + 4 = \pm 5
\]
6. Solve for \(x\) by isolating it:
\[
x + 4 = 5 \quad \Rightarrow \quad x = 5 - 4 \quad \Rightarrow \quad x = 1
\]
\[
x + 4 = -5 \quad \Rightarrow \quad x = -5 - 4 \quad \Rightarrow \quad x = -9
\]
Thus, the two values that solve the quadratic equation \(x^2 + 8x = 9\) are:
\[
x = 1 \quad \text{and} \quad x = -9
\]
1. Move the constant to the right side of the equation:
\[
x^2 + 8x - 9 = 0
\]
2. Rearrange it:
\[
x^2 + 8x = 9
\]
3. To complete the square, take half of the coefficient of \(x\) (which is 8), square it, and add that value to both sides. Half of 8 is 4, and squaring it gives 16:
\[
x^2 + 8x + 16 = 9 + 16
\]
\[
x^2 + 8x + 16 = 25
\]
4. Now, the left side factors as:
\[
(x + 4)^2 = 25
\]
5. Take the square root of both sides:
\[
x + 4 = \pm 5
\]
6. Solve for \(x\) by isolating it:
\[
x + 4 = 5 \quad \Rightarrow \quad x = 5 - 4 \quad \Rightarrow \quad x = 1
\]
\[
x + 4 = -5 \quad \Rightarrow \quad x = -5 - 4 \quad \Rightarrow \quad x = -9
\]
Thus, the two values that solve the quadratic equation \(x^2 + 8x = 9\) are:
\[
x = 1 \quad \text{and} \quad x = -9
\]