Pre-Algebra Examples

$y = x^{2} + 24 x + 16$

Step 1

Rewrite the equation as $x^{2} + 24 x + 16 = y$ .

$x^{2} + 24 x + 16 = y$

Step 2

Subtract $y$ from both sides of the equation.

$x^{2} + 24 x + 16 - y = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 1$ , $b = 24$ , and $c = 16 - y$ into the quadratic formula and solve for $x$ .

$\frac{- 24 \pm \sqrt{24^{2} - 4 \cdot (1 \cdot (16 - y))}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $24$ to the power of $2$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 1 \cdot (16 - y)}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4$ by $1$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot (16 - y)}}{2 \cdot 1}$

Step 5.1.3

Apply the distributive property.

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 16 - 4 (- y)}}{2 \cdot 1}$

Step 5.1.4

Multiply $- 4$ by $16$ .

$x = \frac{- 24 \pm \sqrt{576 - 64 - 4 (- y)}}{2 \cdot 1}$

Step 5.1.5

Multiply $- 1$ by $- 4$ .

$x = \frac{- 24 \pm \sqrt{576 - 64 + 4 y}}{2 \cdot 1}$

Step 5.1.6

Subtract $64$ from $576$ .

$x = \frac{- 24 \pm \sqrt{512 + 4 y}}{2 \cdot 1}$

Step 5.1.7

Factor $4$ out of $512 + 4 y$ .

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Step 5.1.7.1

Factor $4$ out of $512$ .

$x = \frac{- 24 \pm \sqrt{4 \cdot 128 + 4 y}}{2 \cdot 1}$

Step 5.1.7.2

Factor $4$ out of $4 \cdot 128 + 4 y$ .

$x = \frac{- 24 \pm \sqrt{4 (128 + y)}}{2 \cdot 1}$

Step 5.1.8

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

$x = \frac{- 24 \pm \sqrt{2^{2} (128 + y)}}{2 \cdot 1}$

Step 5.1.9

Pull terms out from under the radical.

$x = \frac{- 24 \pm 2 \sqrt{128 + y}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{- 24 \pm 2 \sqrt{128 + y}}{2}$

Step 5.3

Simplify $\frac{- 24 \pm 2 \sqrt{128 + y}}{2}$ .

$x = - 12 \pm \sqrt{128 + y}$

Step 6

The final answer is the combination of both solutions.

$x = - 12 + \sqrt{128 + y}$

$x = - 12 - \sqrt{128 + y}$