Algebra Examples

$- 3 = 4 x^{2} - x - 3$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

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

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Step 1.1.1

Subtract $4 x^{2}$ from both sides of the equation.

$- 3 - 4 x^{2} = - x - 3$

Step 1.1.2

Add $x$ to both sides of the equation.

$- 3 - 4 x^{2} + x = - 3$

Step 1.1.3

Add $3$ to both sides of the equation.

$- 3 - 4 x^{2} + x + 3 = 0$

Step 1.2

Combine the opposite terms in $- 3 - 4 x^{2} + x + 3$ .

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Step 1.2.1

Add $- 3$ and $3$ .

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

Step 1.2.2

Add $- 4 x^{2} + x$ and $0$ .

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

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

One to any power is one.

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

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 4.3

Simplify $\frac{- 1 \pm 1}{- 8}$ .

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

Step 5

The final answer is the combination of both solutions.

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