Algebra Examples

$(8 x - 1) (2 x + 1) = 5 x$

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

Simplify $(8 x - 1) (2 x + 1)$ .

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Step 1.1.1.1

Expand $(8 x - 1) (2 x + 1)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$8 x (2 x + 1) - 1 (2 x + 1) = 5 x$

Step 1.1.1.1.2

Apply the distributive property.

$8 x (2 x) + 8 x \cdot 1 - 1 (2 x + 1) = 5 x$

Step 1.1.1.1.3

Apply the distributive property.

$8 x (2 x) + 8 x \cdot 1 - 1 (2 x) - 1 \cdot 1 = 5 x$

Step 1.1.1.2

Simplify and combine like terms.

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Step 1.1.1.2.1

Simplify each term.

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Step 1.1.1.2.1.1

Rewrite using the commutative property of multiplication.

$8 \cdot 2 x \cdot x + 8 x \cdot 1 - 1 (2 x) - 1 \cdot 1 = 5 x$

Step 1.1.1.2.1.2

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

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Step 1.1.1.2.1.2.1

Move $x$ .

$8 \cdot 2 (x \cdot x) + 8 x \cdot 1 - 1 (2 x) - 1 \cdot 1 = 5 x$

Step 1.1.1.2.1.2.2

Multiply $x$ by $x$ .

$8 \cdot 2 x^{2} + 8 x \cdot 1 - 1 (2 x) - 1 \cdot 1 = 5 x$

Step 1.1.1.2.1.3

Multiply $8$ by $2$ .

$16 x^{2} + 8 x \cdot 1 - 1 (2 x) - 1 \cdot 1 = 5 x$

Step 1.1.1.2.1.4

Multiply $8$ by $1$ .

$16 x^{2} + 8 x - 1 (2 x) - 1 \cdot 1 = 5 x$

Step 1.1.1.2.1.5

Multiply $2$ by $- 1$ .

$16 x^{2} + 8 x - 2 x - 1 \cdot 1 = 5 x$

Step 1.1.1.2.1.6

Multiply $- 1$ by $1$ .

$16 x^{2} + 8 x - 2 x - 1 = 5 x$

Step 1.1.1.2.2

Subtract $2 x$ from $8 x$ .

$16 x^{2} + 6 x - 1 = 5 x$

Step 1.2

Subtract $5 x$ from both sides of the equation.

$16 x^{2} + 6 x - 1 - 5 x = 0$

Step 1.3

Subtract $5 x$ from $6 x$ .

$16 x^{2} + x - 1 = 0$

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

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

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.

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

Step 4.1.2

Multiply $- 4 \cdot 16 \cdot - 1$ .

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Step 4.1.2.1

Multiply $- 4$ by $16$ .

$x = \frac{- 1 \pm \sqrt{1 - 64 \cdot - 1}}{2 \cdot 16}$

Step 4.1.2.2

Multiply $- 64$ by $- 1$ .

$x = \frac{- 1 \pm \sqrt{1 + 64}}{2 \cdot 16}$

Step 4.1.3

Add $1$ and $64$ .

$x = \frac{- 1 \pm \sqrt{65}}{2 \cdot 16}$

Step 4.2

Multiply $2$ by $16$ .

$x = \frac{- 1 \pm \sqrt{65}}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{65}}{32}$

Decimal Form:

$x = 0.22069555 \dots, - 0.28319555 \dots$