Question

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Multiple Answer 1 point
Solve this quadratic equation.
Check all that apply.
x2+10x+25=2
x=-5-J2
x=-5+J2
x=5+12
x=5-J2

Answer 1

To solve the quadratic equation \( x^2 + 10x + 25 = 2 \), we first rewrite it in standard form:

\[ x^2 + 10x + 25 - 2 = 0 \]

This simplifies to:

\[ x^2 + 10x + 23 = 0 \]

Next, we apply the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \( a = 1 \), \( b = 10 \), and \( c = 23 \).

Calculating the discriminant:

\[
b^2 - 4ac = 10^2 - 4 \cdot 1 \cdot 23 = 100 - 92 = 8
\]

Now, substituting back into the quadratic formula:

\[
x = \frac{-10 \pm \sqrt{8}}{2 \cdot 1} = \frac{-10 \pm 2\sqrt{2}}{2} = -5 \pm \sqrt{2}
\]

So the solutions are:

\[
x = -5 + \sqrt{2} \quad \text{and} \quad x = -5 - \sqrt{2}
\]

Looking at the options you provided:

- \( x = -5 - J2 \) (Incorrect, as J represents an imaginary unit and we have a real solution)
- \( x = -5 + J2 \) (Incorrect for the same reason)
- \( x = 5 + 12 \) (Incorrect)
- \( x = 5 - J2 \) (Incorrect)

None of the provided options correctly match the solutions. The correct roots are:

1. \( x = -5 + \sqrt{2} \)
2. \( x = -5 - \sqrt{2} \)

None of the answers provided are applicable.