Question

Solve by inspection. Which two are solutions for x2+8x−15=5 ? CHOOSE TWO. (2 points) Responses x=−10 x is equal to negative 10 x=2 x is equal to 2 x=10 x is equal to 10 x=−2

Answer 1

To solve the equation \( x^2 + 8x - 15 = 5 \) by inspection, we first rewrite it in standard form by moving \( 5 \) to the left side:

\[
x^2 + 8x - 15 - 5 = 0
\]

This simplifies to:

\[
x^2 + 8x - 20 = 0
\]

Next, we can try to factor this quadratic equation. We need to find two numbers that multiply to \(-20\) (the constant term) and add up to \(8\) (the coefficient of \(x\)).

The pairs of factors of \(-20\) are:
- \(1\) and \(-20\)
- \(-1\) and \(20\)
- \(2\) and \(-10\)
- \(-2\) and \(10\)
- \(4\) and \(-5\)
- \(-4\) and \(5\)

Out of these, the pair that adds up to \(8\) is \(-2\) and \(10\). Therefore, we can factor the equation as:

\[
(x - 2)(x + 10) = 0
\]

Setting each factor to zero gives us the solutions:

1. \(x - 2 = 0 \Rightarrow x = 2\)
2. \(x + 10 = 0 \Rightarrow x = -10\)

Thus, the two solutions for the equation \(x^2 + 8x - 15 = 5\) are:

1. \(x = 2\)
2. \(x = -10\)

So the answers are:

- \(x = -10\)
- \(x = 2\)