To solve the equation \((3k + 2)^2 = 100\) using the square root property, we will take the square root of both sides of the equation.
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Start by applying the square root property: \[ 3k + 2 = \pm \sqrt{100} \]
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Calculate \(\sqrt{100}\): \[ \sqrt{100} = 10 \] Therefore, we have: \[ 3k + 2 = \pm 10 \]
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Now we will set up two separate equations based on the \(\pm\) sign:
- Equation 1: \[ 3k + 2 = 10 \]
- Equation 2: \[ 3k + 2 = -10 \]
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Solve the first equation: \[ 3k + 2 = 10 \] Subtract 2 from both sides: \[ 3k = 8 \] Divide by 3: \[ k = \frac{8}{3} \]
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Solve the second equation: \[ 3k + 2 = -10 \] Subtract 2 from both sides: \[ 3k = -12 \] Divide by 3: \[ k = -4 \]
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Therefore, the solutions to the equation \((3k + 2)^2 = 100\) are: \[ k = \frac{8}{3} \quad \text{and} \quad k = -4 \]