Solve 5x^2-22x-48

Question

Factor the expression

(x - 6) (5 x + 8)

Evaluate

5 x^{2} - 22 x - 48

Rewrite the expression

5 x^{2} + (8 - 30) x - 48

Calculate

5 x^{2} + 8 x - 30 x - 48

Rewrite the expression

x \times 5 x + x \times 8 - 6 \times 5 x - 6 \times 8

Factor out x from the expression

x (5 x + 8) - 6 \times 5 x - 6 \times 8

Factor out - 6 from the expression

x (5 x + 8) - 6 (5 x + 8)

Solution

(x - 6) (5 x + 8)

Show Solution

x_{1} = - \frac{8}{5}, x_{2} = 6

Alternative Form

x_{1} = - 1.6, x_{2} = 6

Evaluate

5 x^{2} - 22 x - 48

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

5 x^{2} - 22 x - 48 = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 22 x - 48

Rewrite the expression

5 x^{2} + (8 - 30) x - 48

Calculate

5 x^{2} + 8 x - 30 x - 48

Rewrite the expression

x \times 5 x + x \times 8 - 6 \times 5 x - 6 \times 8

Factor out x from the expression

x (5 x + 8) - 6 \times 5 x - 6 \times 8

Factor out - 6 from the expression

x (5 x + 8) - 6 (5 x + 8)

Factor out 5 x + 8 from the expression

(x - 6) (5 x + 8)

(x - 6) (5 x + 8) = 0

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

x - 6 = 0 5 x + 8 = 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 5 x + 8 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 8 = 0

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

5 x = 0 - 8

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

5 x = - 8

Divide both sides

\frac{5 x}{5} = \frac{- 8}{5}

Divide the numbers

x = \frac{- 8}{5}

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

x = - \frac{8}{5}

x = 6 x = - \frac{8}{5}

Solution

x_{1} = - \frac{8}{5}, x_{2} = 6

Alternative Form

x_{1} = - 1.6, x_{2} = 6

Show Solution