Complete the square to identify the two values that solve the following quadratic equation: x2+8x=9

Question

𝑥
2
+
8
𝑥
=
9
.(1 point)
x=
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=

Answer 1

To solve the quadratic equation \( x^2 + 8x = 9 \) by completing the square, follow these steps:

1. Start with the equation in standard form: \[ x^2 + 8x - 9 = 0 \]

2. Move the constant term to the other side: \[ x^2 + 8x = 9 \]

3. To complete the square, take half of the coefficient of \( x \) (which is 8), square it, and add it to both sides. Half of 8 is 4, and squaring it gives 16: \[ x^2 + 8x + 16 = 9 + 16 \]

4. Now rewrite the left side as a perfect square: \[ (x + 4)^2 = 25 \]

5. Take the square root of both sides: \[ x + 4 = \pm 5 \]

6. Solve for \( x \) by isolating it:

   • For the positive case: \[ x + 4 = 5 \implies x = 5 - 4 = 1 \]
   • For the negative case: \[ x + 4 = -5 \implies x = -5 - 4 = -9 \]

Thus, the two values that solve the quadratic equation are: \[ x = 1 \quad \text{and} \quad x = -9 \]