To determine which of the proposed solutions is correct for the quadratic equation \( 4x^2 + 2x = 10 \), we need to solve the equation first.
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Rearranging the equation: \[ 4x^2 + 2x - 10 = 0 \]
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Using the quadratic formula: The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 4 \), \( b = 2 \), and \( c = -10 \).
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Calculating the discriminant: \[ b^2 - 4ac = 2^2 - 4(4)(-10) = 4 + 160 = 164 \]
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Applying the quadratic formula: \[ x = \frac{-2 \pm \sqrt{164}}{2(4)} \] \[ x = \frac{-2 \pm \sqrt{164}}{8} \] \[ \sqrt{164} \approx 12.81 \] Therefore: \[ x = \frac{-2 \pm 12.81}{8} \]
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Calculating the two possible values:
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First solution: \[ x_1 = \frac{-2 + 12.81}{8} \approx \frac{10.81}{8} \approx 1.35 \]
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Second solution: \[ x_2 = \frac{-2 - 12.81}{8} \approx \frac{-14.81}{8} \approx -1.85 \]
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Conclusion: The solutions are approximately \( x \approx 1.35 \) and \( x \approx -1.85 \).
From the proposed answers:
- \( x = 1.04 \) is incorrect based on this calculation, as it does not match the calculated value of approximately \( 1.35 \).
- \( x = -1.85 \) is correct, as it matches the calculated approximate solution.
In summary, \( x = 1.04 \) is wrong because it doesn't satisfy the equation, while \( x = -1.85 \) is a correct solution.