Algebra Examples

$72 = (8 x + 3) (8 x - 3)$

Step 1

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

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Step 1.1

Simplify the right side.

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Step 1.1.1

Simplify $(8 x + 3) (8 x - 3)$ .

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Step 1.1.1.1

Expand $(8 x + 3) (8 x - 3)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$72 = 8 x (8 x - 3) + 3 (8 x - 3)$

Step 1.1.1.1.2

Apply the distributive property.

$72 = 8 x (8 x) + 8 x \cdot - 3 + 3 (8 x - 3)$

Step 1.1.1.1.3

Apply the distributive property.

$72 = 8 x (8 x) + 8 x \cdot - 3 + 3 (8 x) + 3 \cdot - 3$

Step 1.1.1.2

Simplify terms.

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Step 1.1.1.2.1

Combine the opposite terms in $8 x (8 x) + 8 x \cdot - 3 + 3 (8 x) + 3 \cdot - 3$ .

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Step 1.1.1.2.1.1

Reorder the factors in the terms $8 x \cdot - 3$ and $3 (8 x)$ .

$72 = 8 x (8 x) - 3 \cdot 8 x + 3 \cdot 8 x + 3 \cdot - 3$

Step 1.1.1.2.1.2

Add $- 3 \cdot 8 x$ and $3 \cdot 8 x$ .

$72 = 8 x (8 x) + 0 + 3 \cdot - 3$

Step 1.1.1.2.1.3

Add $8 x (8 x)$ and $0$ .

$72 = 8 x (8 x) + 3 \cdot - 3$

Step 1.1.1.2.2

Simplify each term.

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Step 1.1.1.2.2.1

Rewrite using the commutative property of multiplication.

$72 = 8 \cdot 8 x \cdot x + 3 \cdot - 3$

Step 1.1.1.2.2.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.1.2.2.2.1

Move $x$ .

$72 = 8 \cdot 8 (x \cdot x) + 3 \cdot - 3$

Step 1.1.1.2.2.2.2

Multiply $x$ by $x$ .

$72 = 8 \cdot 8 x^{2} + 3 \cdot - 3$

Step 1.1.1.2.2.3

Multiply $8$ by $8$ .

$72 = 64 x^{2} + 3 \cdot - 3$

Step 1.1.1.2.2.4

Multiply $3$ by $- 3$ .

$72 = 64 x^{2} - 9$

Step 1.2

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

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Step 1.2.1

Subtract $64 x^{2}$ from both sides of the equation.

$72 - 64 x^{2} = - 9$

Step 1.2.2

Add $9$ to both sides of the equation.

$72 - 64 x^{2} + 9 = 0$

Step 1.3

Add $72$ and $9$ .

$- 64 x^{2} + 81 = 0$

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 $a = - 64$ , $b = 0$ , and $c = 81$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 64 \cdot 81)}}{2 \cdot - 64}$

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 $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 64 \cdot 81}}{2 \cdot - 64}$

Step 4.1.2

Multiply $- 4 \cdot - 64 \cdot 81$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 64$ .

$x = \frac{0 \pm \sqrt{0 + 256 \cdot 81}}{2 \cdot - 64}$

Step 4.1.2.2

Multiply $256$ by $81$ .

$x = \frac{0 \pm \sqrt{0 + 20736}}{2 \cdot - 64}$

Step 4.1.3

Add $0$ and $20736$ .

$x = \frac{0 \pm \sqrt{20736}}{2 \cdot - 64}$

Step 4.1.4

Rewrite $20736$ as $144^{2}$ .

$x = \frac{0 \pm \sqrt{144^{2}}}{2 \cdot - 64}$

Step 4.1.5

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

$x = \frac{0 \pm 144}{2 \cdot - 64}$

Step 4.2

Multiply $2$ by $- 64$ .

$x = \frac{0 \pm 144}{- 128}$

Step 4.3

Simplify $\frac{0 \pm 144}{- 128}$ .

$x = \frac{\pm 9}{8}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{9}{8}, - \frac{9}{8}$