Question

Solve by inspection. Which two are solutions for x2+8x−15=5
𝑥
2
+
8
𝑥
−
15
=
5
?(2 points)
Responses

x=10
𝑥
=
10
x is equal to 10

x=2
𝑥
=
2
x is equal to 2

x=−2
𝑥
=
−
2
x is equal to negative 2

x=−10

Answer 1

To solve the equation \( x^2 + 8x - 15 = 5 \) by inspection, first, we can simplify the equation by moving all terms to one side:

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

This simplifies to:

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

Next, we can factor the quadratic equation or look for integer solutions that would satisfy the equation.

We need two numbers that multiply to \(-20\) and add to \(8\). The pairs of factors of \(-20\) are:

- \(1\) and \(-20\) (adds to \(-19\))
- \(-1\) and \(20\) (adds to \(19\))
- \(2\) and \(-10\) (adds to \(-8\))
- \(-2\) and \(10\) (adds to \(8\))
- \(4\) and \(-5\) (adds to \(-1\))
- \(-4\) and \(5\) (adds to \(1\))

The pair that works is \(-2\) and \(10\).

So, the solutions to the equation \(x^2 + 8x - 20 = 0\) are:

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

Thus, the two solutions from the provided options are:

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