To solve the quadratic equation \((5x + 6)^2 + 24 = 33\), we can follow these steps:
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Isolate the squared term: \[ (5x + 6)^2 + 24 - 24 = 33 - 24 \] Simplifying this gives: \[ (5x + 6)^2 = 9 \]
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Take the square root of both sides: \[ 5x + 6 = \pm 3 \]
This results in two separate equations to solve:
- \(5x + 6 = 3\)
- \(5x + 6 = -3\)
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Solve each equation:
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For the first equation \(5x + 6 = 3\): \[ 5x = 3 - 6 \] \[ 5x = -3 \] \[ x = -\frac{3}{5} \]
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For the second equation \(5x + 6 = -3\): \[ 5x = -3 - 6 \] \[ 5x = -9 \] \[ x = -\frac{9}{5} \]
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Final solutions: The values of \(x\) that solve the equation are: \[ x = -\frac{3}{5} \quad \text{and} \quad x = -\frac{9}{5} \]
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