Question

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

Answer 1

Answer:

$x = 2 + \sqrt{42}$   or   $x = 2 - \sqrt{42}$

Step-by-step 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

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-38)}}{2(1)}$

$x = \dfrac{4 \pm \sqrt{16 + 152}}{2}$

$x = \dfrac{4 \pm \sqrt{168}}{2}$

$x = 2 \pm \dfrac{\sqrt{4 \times 42}}{2}$

$x = 2 \pm \dfrac{2\sqrt{42}}{2}$

$x = 2 \pm \sqrt{42}$

$x = 2 + \sqrt{42}$   or   $x = 2 - \sqrt{42}$