Algebra Examples

$4 x^{2} = x$

Step 1

Subtract $x$ from both sides of the equation.

$4 x^{2} - x = 0$

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 $a = 4$ , $b = - 1$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (4 \cdot 0)}}{2 \cdot 4}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 4 \cdot 0}}{2 \cdot 4}$

Step 4.1.2

Multiply $- 4 \cdot 4 \cdot 0$ .

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Step 4.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{1 \pm \sqrt{1 - 16 \cdot 0}}{2 \cdot 4}$

Step 4.1.2.2

Multiply $- 16$ by $0$ .

$x = \frac{1 \pm \sqrt{1 + 0}}{2 \cdot 4}$

Step 4.1.3

Add $1$ and $0$ .

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

Step 4.1.4

Any root of $1$ is $1$ .

$x = \frac{1 \pm 1}{2 \cdot 4}$

Step 4.2

Multiply $2$ by $4$ .

$x = \frac{1 \pm 1}{8}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{1}{4}, 0$