Solve 8x^2 -19x -15

Question

8 x^{2} - 19 x - 15

Factor the expression

(x - 3) (8 x + 5)

Evaluate

8 x^{2} - 19 x - 15

Rewrite the expression

8 x^{2} + (5 - 24) x - 15

Calculate

8 x^{2} + 5 x - 24 x - 15

Rewrite the expression

x \times 8 x + x \times 5 - 3 \times 8 x - 3 \times 5

Factor out x from the expression

x (8 x + 5) - 3 \times 8 x - 3 \times 5

Factor out - 3 from the expression

x (8 x + 5) - 3 (8 x + 5)

Solution

(x - 3) (8 x + 5)

Show Solution

x_{1} = - \frac{5}{8}, x_{2} = 3

Alternative Form

x_{1} = - 0.625, x_{2} = 3

Evaluate

8 x^{2} - 19 x - 15

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

8 x^{2} - 19 x - 15 = 0

Factor the expression

More Steps

Evaluate

8 x^{2} - 19 x - 15

Rewrite the expression

8 x^{2} + (5 - 24) x - 15

Calculate

8 x^{2} + 5 x - 24 x - 15

Rewrite the expression

x \times 8 x + x \times 5 - 3 \times 8 x - 3 \times 5

Factor out x from the expression

x (8 x + 5) - 3 \times 8 x - 3 \times 5

Factor out - 3 from the expression

x (8 x + 5) - 3 (8 x + 5)

Factor out 8 x + 5 from the expression

(x - 3) (8 x + 5)

(x - 3) (8 x + 5) = 0

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

x - 3 = 0 8 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 8 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

8 x + 5 = 0

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

8 x = 0 - 5

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

8 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{8}

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

x = - \frac{5}{8}

x = 3 x = - \frac{5}{8}

Solution

x_{1} = - \frac{5}{8}, x_{2} = 3

Alternative Form

x_{1} = - 0.625, x_{2} = 3

Show Solution