Question

Solve for x in the equation x2 - 4x - 9 = 29.

Answer 1

`x = 2 + √(42)` or
`x = 2 - √(42)`

Explanation:

`x^2 - 4x - 9 = 29`

Subtract 29 from both sides.

`x^2 - 4x - 9 - 29 = 29 - 29`

`x^2 - 4x - 38 = 0`

There are no two integers whose sum is -4 and whose product is -38, so the trinomial is not factorable. We can use the quadratic formula.

a = 1; b = -4; c = -38

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-(-4) \pm √((-4)^2 - 4(1)(-38)))/(2(1))`

`x = (4 \pm √(16 + 152))/(2)`

`x = (4 \pm √(168))/(2)`

`x = 2 \pm (√(4 * 42))/(2)`

`x = 2 \pm (2√(42))/(2)`

`x = 2 \pm √(42)`

`x = 2 + √(42)` or
`x = 2 - √(42)`