Question

What values of x make the equation x2 + 9x – 22 = 0 true?

Answer 1

Answer:

2 and -11

Step-by-step explanation:

Step 1: Use the quadratic formula to solve for x

$x=\frac{-b+-\sqrt{b^{2-4ac} } }{2a} \\x=\frac{-9+-\sqrt{9^{2}-4(1) (-22)} }{2(1)} \\x=\frac{-9+-\sqrt{169} }{2(1)}\\x=\frac{-9+-13 }{2}\\x1=\frac{-9+13 }{2}\\x1=\frac{4}{2} \\x1 = 2\\x2 = \frac{-9-13 }{2}\\x2 = \frac{-22 }{2}\\x2 = -11$

Therefore the values of 'x' that make the equation true is 2 and -11

Answer 2

To solve this polynomial equation, we will need to factor the left side.

On the left, we have a a trinomial in a special form that

can be factored as the product of two binomials.

The trinomial on the left can be factored which makes life easier.

This factors as (x + 11)(x - 2) = 0.

This means that either x + 11 = 0 or x - 2 = 0.

Solving each equation from here, we get x = -11 or x = 2.

So the solution is {-11, 2}.