Completing the Square & the Quadratic Formula Practice

Question

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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

Answer 1

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: \[ x = 1 \quad \text{and} \quad x = -9 \]