Algebra Examples

$x^{2} - 3 x + 2 = 0$

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

$a = 1$ ,

$b = - 3$ , and

$c = 2$ into the quadratic formula and solve for

$x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (1 \cdot 2)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise

$- 3$ to the power of

$2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 1 \cdot 2}}{2 \cdot 1}$

Step 3.1.2

Multiply

$- 4 \cdot 1 \cdot 2$ .

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Step 3.1.2.1

Multiply

$- 4$ by

$1$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 2}}{2 \cdot 1}$

Step 3.1.2.2

Multiply

$- 4$ by

$2$ .

$x = \frac{3 \pm \sqrt{9 - 8}}{2 \cdot 1}$

Step 3.1.3

Subtract

$8$ from

$9$ .

$x = \frac{3 \pm \sqrt{1}}{2 \cdot 1}$

Step 3.1.4

Any root of

$1$ is

$1$ .

$x = \frac{3 \pm 1}{2 \cdot 1}$

Step 3.2

Multiply

$2$ by

$1$ .

$x = \frac{3 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 2, 1$