Solve Using the Quadratic Formula

$x^{2} - 5 x + 6 = 0$

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 $a = 1$ , $b = - 5$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (1 \cdot 6)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$

Step 3.1.2

Multiply $- 4 \cdot 1 \cdot 6$ .

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 6}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $6$ .

$x = \frac{5 \pm \sqrt{25 - 24}}{2 \cdot 1}$

Step 3.1.3

Subtract $24$ from $25$ .

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

Step 3.1.4

Any root of $1$ is $1$ .

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

Step 3.2

Multiply $2$ by $1$ .

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

Step 4

The final answer is the combination of both solutions.

$x = 3, 2$

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