To solve the quadratic equation \( x^2 + 8x = 9 \) by completing the square, follow these steps:
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Move 9 to the left side of the equation:
\[ x^2 + 8x - 9 = 0 \]
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Isolate the quadratic and linear terms:
\[ x^2 + 8x = 9 \]
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Complete the square:
To complete the square for the expression \( x^2 + 8x \), take half of the coefficient of \( x \) (which is 8), square it, and add it to both sides of the equation. Half of 8 is 4, and squaring it gives 16.
\[ x^2 + 8x + 16 = 9 + 16 \]
Simplifying both sides:
\[ x^2 + 8x + 16 = 25 \]
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Factor the left side:
\[ (x + 4)^2 = 25 \]
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Take the square root of both sides:
\[ x + 4 = \pm 5 \]
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Solve for \( x \):
From \( x + 4 = 5 \):
\[ x = 5 - 4 = 1 \]
From \( x + 4 = -5 \):
\[ x = -5 - 4 = -9 \]
Thus, the two values that solve the quadratic equation \( x^2 + 8x = 9 \) are:
\[ x = 1 \quad \text{and} \quad x = -9 \]
If you are looking to fill in the answer:
x = 1 or x = -9