Solve Using the Quadratic Formula x^2-11x+19=-5

$x^{2} - 11 x + 19 = - 5$

Step 1

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

Add $5$ to both sides of the equation.

$x^{2} - 11 x + 19 + 5 = 0$

Add $19$ and $5$ .

$x^{2} - 11 x + 24 = 0$

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 $a = 1$ , $b = - 11$ , and $c = 24$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (1 \cdot 24)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 1 \cdot 24}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 24$ .

Multiply $- 4$ by $1$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 24}}{2 \cdot 1}$

Multiply $- 4$ by $24$ .

$x = \frac{11 \pm \sqrt{121 - 96}}{2 \cdot 1}$

Subtract $96$ from $121$ .

$x = \frac{11 \pm \sqrt{25}}{2 \cdot 1}$

Rewrite $25$ as $5^{2}$ .

$x = \frac{11 \pm \sqrt{5^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{11 \pm 5}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{11 \pm 5}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 8, 3$