Algebra Examples

$x^{2} - 9 x - 10 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 1$ , $b = - 9$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot - 10)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot - 10}}{2 \cdot 1}$

Step 3.1.2

Multiply $- 4 \cdot 1 \cdot - 10$ .

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot - 10}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $- 10$ .

$x = \frac{9 \pm \sqrt{81 + 40}}{2 \cdot 1}$

Step 3.1.3

Add $81$ and $40$ .

$x = \frac{9 \pm \sqrt{121}}{2 \cdot 1}$

Step 3.1.4

Rewrite $121$ as $11^{2}$ .

$x = \frac{9 \pm \sqrt{11^{2}}}{2 \cdot 1}$

Step 3.1.5

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

$x = \frac{9 \pm 11}{2 \cdot 1}$

Step 3.2

Multiply $2$ by $1$ .

$x = \frac{9 \pm 11}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 10, - 1$