To solve the quadratic equation \( x^2 + 8x = 9 \) by completing the square, follow these steps:
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Move the constant to the other side of the equation: \[ x^2 + 8x - 9 = 0 \]
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Rearrange to focus on the quadratic and linear terms: \[ x^2 + 8x = 9 \]
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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: \[ x^2 + 8x + 16 = 9 + 16 \]
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Simplify both sides: \[ (x + 4)^2 = 25 \]
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Take the square root of both sides: \[ x + 4 = 5 \quad \text{or} \quad x + 4 = -5 \]
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Solve for \( x \) in both cases:
- For \( x + 4 = 5 \): \[ x = 5 - 4 = 1 \]
- For \( x + 4 = -5 \): \[ x = -5 - 4 = -9 \]
Thus, the solutions to the equation \( x^2 + 8x = 9 \) are: \[ x = 1 \quad \text{and} \quad x = -9 \]
So, the answers are \( x = 1 \) and \( x = -9 \).
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