Solve 64x^2-64x-9

Question

Factor the expression

(8 x - 9) (8 x + 1)

Evaluate

64 x^{2} - 64 x - 9

Rewrite the expression

64 x^{2} + (8 - 72) x - 9

Calculate

64 x^{2} + 8 x - 72 x - 9

Rewrite the expression

8 x \times 8 x + 8 x - 9 \times 8 x - 9

Factor out 8 x from the expression

8 x (8 x + 1) - 9 \times 8 x - 9

Factor out - 9 from the expression

8 x (8 x + 1) - 9 (8 x + 1)

Solution

(8 x - 9) (8 x + 1)

Show Solution

x_{1} = - \frac{1}{8}, x_{2} = \frac{9}{8}

Alternative Form

x_{1} = - 0.125, x_{2} = 1.125

Evaluate

64 x^{2} - 64 x - 9

To find the roots of the expression,set the expression equal to 0

64 x^{2} - 64 x - 9 = 0

Factor the expression

More Steps

Evaluate

64 x^{2} - 64 x - 9

Rewrite the expression

64 x^{2} + (8 - 72) x - 9

Calculate

64 x^{2} + 8 x - 72 x - 9

Rewrite the expression

8 x \times 8 x + 8 x - 9 \times 8 x - 9

Factor out 8 x from the expression

8 x (8 x + 1) - 9 \times 8 x - 9

Factor out - 9 from the expression

8 x (8 x + 1) - 9 (8 x + 1)

Factor out 8 x + 1 from the expression

(8 x - 9) (8 x + 1)

(8 x - 9) (8 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

8 x - 9 = 0 8 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

8 x - 9 = 0

Move the constant to the right-hand side and change its sign

8 x = 0 + 9

Removing 0 doesn't change the value,so remove it from the expression

8 x = 9

Divide both sides

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

Divide the numbers

x = \frac{9}{8}

x = \frac{9}{8} 8 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

8 x + 1 = 0

Move the constant to the right-hand side and change its sign

8 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

8 x = - 1

Divide both sides

\frac{8 x}{8} = \frac{- 1}{8}

Divide the numbers

x = \frac{- 1}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{8}

x = \frac{9}{8} x = - \frac{1}{8}

Solution

x_{1} = - \frac{1}{8}, x_{2} = \frac{9}{8}

Alternative Form

x_{1} = - 0.125, x_{2} = 1.125

Show Solution