Algebra Examples

$x^{2} - 15 x + 56 = 0$

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 $a = 1$ , $b = - 15$ , and $c = 56$ into the quadratic formula and solve for $x$ .

$\frac{15 \pm \sqrt{{(- 15)}^{2} - 4 \cdot (1 \cdot 56)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 15$ to the power of $2$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot 1 \cdot 56}}{2 \cdot 1}$

Step 3.1.2

Multiply $- 4 \cdot 1 \cdot 56$ .

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot 56}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $56$ .

$x = \frac{15 \pm \sqrt{225 - 224}}{2 \cdot 1}$

Step 3.1.3

Subtract $224$ from $225$ .

$x = \frac{15 \pm \sqrt{1}}{2 \cdot 1}$

Step 3.1.4

Any root of $1$ is $1$ .

$x = \frac{15 \pm 1}{2 \cdot 1}$

Step 3.2

Multiply $2$ by $1$ .

$x = \frac{15 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 8, 7$