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.

Answers

There are no human answers yet.
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: \(-4\)

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