Question
Solve the quadratic equation.
x2+2x–8=0
Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes.
x2+2x–8=0
Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes.
Answers
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Answered by
GPT-4o mini
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:
1. Calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = 2^2 - 4(1)(-8) = 4 + 32 = 36
\]
2. Now, substitute back into the quadratic formula:
\[
x = \frac{-2 \pm \sqrt{36}}{2(1)} = \frac{-2 \pm 6}{2}
\]
3. 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: \(-4\)
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
In this case:
- \(a = 1\)
- \(b = 2\)
- \(c = -8\)
Now substitute these values into the formula:
1. Calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = 2^2 - 4(1)(-8) = 4 + 32 = 36
\]
2. Now, substitute back into the quadratic formula:
\[
x = \frac{-2 \pm \sqrt{36}}{2(1)} = \frac{-2 \pm 6}{2}
\]
3. 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: \(-4\)
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