Solve Using the Quadratic Formula x^2-4x-9=29

$x^{2} - 4 x - 9 = 29$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $29$ from both sides of the equation.

$x^{2} - 4 x - 9 - 29 = 0$

Subtract $29$ from $- 9$ .

$x^{2} - 4 x - 38 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 4$ , and $c = - 38$ into the quadratic formula and solve for $x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot - 38)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 38}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 38$ .

Multiply $- 4$ by $1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot - 38}}{2 \cdot 1}$

Multiply $- 4$ by $- 38$ .

$x = \frac{4 \pm \sqrt{16 + 152}}{2 \cdot 1}$

Add $16$ and $152$ .

$x = \frac{4 \pm \sqrt{168}}{2 \cdot 1}$

Rewrite $168$ as $2^{2} \cdot 42$ .

Factor $4$ out of $168$ .

$x = \frac{4 \pm \sqrt{4 (42)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{4 \pm \sqrt{2^{2} \cdot 42}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{4 \pm 2 \sqrt{42}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{4 \pm 2 \sqrt{42}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{42}}{2}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 8.48074069 \dots, - 4.48074069 \dots$