Algebra Examples

$x^{2} = 3 x - 1$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$x^{2} - 3 x = - 1$

Step 1.2

Add $1$ to both sides of the equation.

$x^{2} - 3 x + 1 = 0$

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 $a = 1$ , $b = - 3$ , and $c = 1$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 3$ to the power of $2$ .

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

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

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

Step 4.1.2.2

Multiply $- 4$ by $1$ .

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

Step 4.1.3

Subtract $4$ from $9$ .

$x = \frac{3 \pm \sqrt{5}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{3 \pm \sqrt{5}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{5}}{2}$

Decimal Form:

$x = 2.61803398 \dots, 0.38196601 \dots$