Algebra Examples

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

Step 1

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

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Step 1.1

Add $4 x$ to both sides of the equation.

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

Step 1.2

Add $3$ to both sides of the equation.

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

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 $a = 1$ , $b = 4$ , and $c = - y + 3$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot (- y + 3)}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot (- y + 3)}}{2 \cdot 1}$

Step 4.1.3

Apply the distributive property.

$x = \frac{- 4 \pm \sqrt{16 - 4 (- y) - 4 \cdot 3}}{2 \cdot 1}$

Step 4.1.4

Multiply $- 1$ by $- 4$ .

$x = \frac{- 4 \pm \sqrt{16 + 4 y - 4 \cdot 3}}{2 \cdot 1}$

Step 4.1.5

Multiply $- 4$ by $3$ .

$x = \frac{- 4 \pm \sqrt{16 + 4 y - 12}}{2 \cdot 1}$

Step 4.1.6

Subtract $12$ from $16$ .

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

Step 4.1.7

Factor $4$ out of $4 y + 4$ .

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Step 4.1.7.1

Factor $4$ out of $4 y$ .

$x = \frac{- 4 \pm \sqrt{4 (y) + 4}}{2 \cdot 1}$

Step 4.1.7.2

Factor $4$ out of $4$ .

$x = \frac{- 4 \pm \sqrt{4 (y) + 4 (1)}}{2 \cdot 1}$

Step 4.1.7.3

Factor $4$ out of $4 (y) + 4 (1)$ .

$x = \frac{- 4 \pm \sqrt{4 (y + 1)}}{2 \cdot 1}$

Step 4.1.8

Rewrite $4 (y + 1)$ as $2^{2} (y + 1^{2})$ .

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Step 4.1.8.1

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm \sqrt{2^{2} (y + 1)}}{2 \cdot 1}$

Step 4.1.8.2

Rewrite $1$ as $1^{2}$ .

$x = \frac{- 4 \pm \sqrt{2^{2} (y + 1^{2})}}{2 \cdot 1}$

Step 4.1.9

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{y + 1^{2}}}{2 \cdot 1}$

Step 4.1.10

One to any power is one.

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

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 \sqrt{y + 1}}{2}$

Step 4.3

Simplify $\frac{- 4 \pm 2 \sqrt{y + 1}}{2}$ .

$x = - 2 \pm \sqrt{y + 1}$