Solve 5x^2- 37x - 24 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0.6, x_{2} = 8

Evaluate

5 x^{2} - 37 x - 24 = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 37 x - 24

Rewrite the expression

5 x^{2} + (3 - 40) x - 24

Calculate

5 x^{2} + 3 x - 40 x - 24

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 8 from the expression

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

Factor out 5 x + 3 from the expression

(x - 8) (5 x + 3)

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

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

x - 8 = 0 5 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x - 8 = 0

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

x = 0 + 8

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

x = 8

x = 8 5 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 3 = 0

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

5 x = 0 - 3

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

5 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{5}

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

x = - \frac{3}{5}

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

Solution

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

Alternative Form

x_{1} = - 0.6, x_{2} = 8

Show Solution