To solve the quadratic equation \(x^2 + 5x - 10 = 0\) by completing the square, follow these steps:
1. **Move the constant term to the other side of the equation:**
\[
x^2 + 5x = 10
\]
2. **Complete the square on the left side:**
- Take half of the coefficient of \(x\), which is \(\frac{5}{2}\), and square it. This gives \(\left(\frac{5}{2}\right)^2 = \frac{25}{4} = 6.25\).
- Add this value to both sides of the equation:
\[
x^2 + 5x + 6.25 = 10 + 6.25
\]
\[
x^2 + 5x + 6.25 = 16.25
\]
3. **Rewrite the left side as a squared binomial:**
\[
\left(x + \frac{5}{2}\right)^2 = 16.25
\]
\[
\left(x + 2.5\right)^2 = 16.25
\]
4. **Take the square root of both sides:**
\[
x + 2.5 = \pm \sqrt{16.25}
\]
5. **Simplify the square root:**
\[
\sqrt{16.25} \approx 4.03
\]
Thus, we have:
\[
x + 2.5 = 4.03 \quad \text{or} \quad x + 2.5 = -4.03
\]
6. **Solve for \(x\) in each case:**
- For \(x + 2.5 = 4.03\):
\[
x = 4.03 - 2.5
\]
\[
x \approx 1.53
\]
- For \(x + 2.5 = -4.03\):
\[
x = -4.03 - 2.5
\]
\[
x \approx -6.53
\]
So, the solutions to the equation \(x^2 + 5x - 10 = 0\) are approximately \(x = 1.53\) and \(x = -6.53\).
Thus, the correct answer is:
1.53, -6.53
10.
Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x2 + 5x – 10 = 0
1.53, –6.53
1.04, –6.04
–18.75, 13.75
1.94, 4.03
1 answer