Solve 13x^(2)-72x-36

Question

Factor the expression

(x - 6) (13 x + 6)

Evaluate

13 x^{2} - 72 x - 36

Rewrite the expression

13 x^{2} + (6 - 78) x - 36

Calculate

13 x^{2} + 6 x - 78 x - 36

Rewrite the expression

x \times 13 x + x \times 6 - 6 \times 13 x - 6 \times 6

Factor out x from the expression

x (13 x + 6) - 6 \times 13 x - 6 \times 6

Factor out - 6 from the expression

x (13 x + 6) - 6 (13 x + 6)

Solution

(x - 6) (13 x + 6)

Show Solution

x_{1} = - \frac{6}{13}, x_{2} = 6

Alternative Form

x_{1} = - 0. \dot{4} 6153 \dot{8}, x_{2} = 6

Evaluate

13 x^{2} - 72 x - 36

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

13 x^{2} - 72 x - 36 = 0

Factor the expression

More Steps

Evaluate

13 x^{2} - 72 x - 36

Rewrite the expression

13 x^{2} + (6 - 78) x - 36

Calculate

13 x^{2} + 6 x - 78 x - 36

Rewrite the expression

x \times 13 x + x \times 6 - 6 \times 13 x - 6 \times 6

Factor out x from the expression

x (13 x + 6) - 6 \times 13 x - 6 \times 6

Factor out - 6 from the expression

x (13 x + 6) - 6 (13 x + 6)

Factor out 13 x + 6 from the expression

(x - 6) (13 x + 6)

(x - 6) (13 x + 6) = 0

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

x - 6 = 0 13 x + 6 = 0

Solve the equation for x

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 6 13 x + 6 = 0

Solve the equation for x

More Steps

Evaluate

13 x + 6 = 0

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

13 x = 0 - 6

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

13 x = - 6

Divide both sides

\frac{13 x}{13} = \frac{- 6}{13}

Divide the numbers

x = \frac{- 6}{13}

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

x = - \frac{6}{13}

x = 6 x = - \frac{6}{13}

Solution

x_{1} = - \frac{6}{13}, x_{2} = 6

Alternative Form

x_{1} = - 0. \dot{4} 6153 \dot{8}, x_{2} = 6

Show Solution