Algebra Examples

$3 w \cdot w = 48$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Multiply $w$ by $w$ by adding the exponents.

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Step 1.1.1.1

Move $w$ .

$3 (w \cdot w) = 48$

Step 1.1.1.2

Multiply $w$ by $w$ .

$3 w^{2} = 48$

Step 1.2

Subtract $48$ from both sides of the equation.

$3 w^{2} - 48 = 0$

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 $a = 3$ , $b = 0$ , and $c = - 48$ into the quadratic formula and solve for $w$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 48)}}{2 \cdot 3}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$w = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 48}}{2 \cdot 3}$

Step 4.1.2

Multiply $- 4 \cdot 3 \cdot - 48$ .

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Step 4.1.2.1

Multiply $- 4$ by $3$ .

$w = \frac{0 \pm \sqrt{0 - 12 \cdot - 48}}{2 \cdot 3}$

Step 4.1.2.2

Multiply $- 12$ by $- 48$ .

$w = \frac{0 \pm \sqrt{0 + 576}}{2 \cdot 3}$

Step 4.1.3

Add $0$ and $576$ .

$w = \frac{0 \pm \sqrt{576}}{2 \cdot 3}$

Step 4.1.4

Rewrite $576$ as $24^{2}$ .

$w = \frac{0 \pm \sqrt{24^{2}}}{2 \cdot 3}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$w = \frac{0 \pm 24}{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$w = \frac{0 \pm 24}{6}$

Step 4.3

Simplify $\frac{0 \pm 24}{6}$ .

$w = \pm 4$

Step 5

The final answer is the combination of both solutions.

$w = 4, - 4$