Solve 8x^(2)-14x-15

Question

Factor the expression

(2 x - 5) (4 x + 3)

Evaluate

8 x^{2} - 14 x - 15

Rewrite the expression

8 x^{2} + (6 - 20) x - 15

Calculate

8 x^{2} + 6 x - 20 x - 15

Rewrite the expression

2 x \times 4 x + 2 x \times 3 - 5 \times 4 x - 5 \times 3

Factor out 2 x from the expression

2 x (4 x + 3) - 5 \times 4 x - 5 \times 3

Factor out - 5 from the expression

2 x (4 x + 3) - 5 (4 x + 3)

Solution

(2 x - 5) (4 x + 3)

Show Solution

x_{1} = - \frac{3}{4}, x_{2} = \frac{5}{2}

Alternative Form

x_{1} = - 0.75, x_{2} = 2.5

Evaluate

8 x^{2} - 14 x - 15

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

8 x^{2} - 14 x - 15 = 0

Factor the expression

More Steps

Evaluate

8 x^{2} - 14 x - 15

Rewrite the expression

8 x^{2} + (6 - 20) x - 15

Calculate

8 x^{2} + 6 x - 20 x - 15

Rewrite the expression

2 x \times 4 x + 2 x \times 3 - 5 \times 4 x - 5 \times 3

Factor out 2 x from the expression

2 x (4 x + 3) - 5 \times 4 x - 5 \times 3

Factor out - 5 from the expression

2 x (4 x + 3) - 5 (4 x + 3)

Factor out 4 x + 3 from the expression

(2 x - 5) (4 x + 3)

(2 x - 5) (4 x + 3) = 0

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

2 x - 5 = 0 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

\frac{2 x}{2} = \frac{5}{2}

Divide the numbers

x = \frac{5}{2}

x = \frac{5}{2} 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 3 = 0

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

4 x = 0 - 3

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

4 x = - 3

Divide both sides

\frac{4 x}{4} = \frac{- 3}{4}

Divide the numbers

x = \frac{- 3}{4}

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

x = - \frac{3}{4}

x = \frac{5}{2} x = - \frac{3}{4}

Solution

x_{1} = - \frac{3}{4}, x_{2} = \frac{5}{2}

Alternative Form

x_{1} = - 0.75, x_{2} = 2.5

Show Solution