Question

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

Answer 1

2 and -11

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=(-9+-√(169) )/(2(1))\\x=(-9+-13 )/(2)\\x1=(-9+13 )/(2)\\x1=(4)/(2) \\x1 = 2\\x2 = (-9-13 )/(2)\\x2 = (-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}.