To solve the quadratic equation \(x^2 + 2x - 8 = 0\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case:
- \(a = 1\)
- \(b = 2\)
- \(c = -8\)
Now substitute these values into the formula:
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Calculate the discriminant \(b^2 - 4ac\): \[ b^2 - 4ac = 2^2 - 4(1)(-8) = 4 + 32 = 36 \]
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Now, substitute back into the quadratic formula: \[ x = \frac{-2 \pm \sqrt{36}}{2(1)} = \frac{-2 \pm 6}{2} \]
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This gives us two solutions: \[ x = \frac{-2 + 6}{2} = \frac{4}{2} = 2 \] \[ x = \frac{-2 - 6}{2} = \frac{-8}{2} = -4 \]
Therefore, the exact solutions to the equation \(x^2 + 2x - 8 = 0\) are:
- \(x = 2\)
- \(x = -4\)
You can put these solutions in the boxes as follows:
- Box 1: \(2\)
- Box 2: \(-4\)