Question

How do you solve `x^2 + 5x + 3 = 9`?

Answer 1

`x = -6, x = 1`

Explanation:

Given: `x^2 + 5x + 3 = 9`

Solve means to find the values of `x` that make the equation true.

Put the equation in the form: `Ax^2 + Bx + C = 0` by subtraction `9` from both sides of the equation:

`x^2 + 5x -6 = 0`

Factor the equation by finding two numbers that multiply to

`ul(A*C = -6 " and sum to " B = 5)`
`-2 * 3 = -6 " "-2+3 = 1" doesn't work"`
`-6 * 1 = -6 " "-6 + 1 = -5" doesn't work"`
`6 * -1 = -6 " " 6 + -1 = 5" works"`

`x^2 + 5x -6 = 0 => " "(x+6)(x-1) = 0`

`x + 6 = 0; " " x - 1 = 0`

`x = -6, x = 1`