Solve 9x^2-155x-500=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{25}{9}, x_{2} = 20

Alternative Form

x_{1} = - 2. \dot{7}, x_{2} = 20

Evaluate

9 x^{2} - 155 x - 500 = 0

Factor the expression

More Steps

Evaluate

9 x^{2} - 155 x - 500

Rewrite the expression

9 x^{2} + (25 - 180) x - 500

Calculate

9 x^{2} + 25 x - 180 x - 500

Rewrite the expression

x \times 9 x + x \times 25 - 20 \times 9 x - 20 \times 25

Factor out x from the expression

x (9 x + 25) - 20 \times 9 x - 20 \times 25

Factor out - 20 from the expression

x (9 x + 25) - 20 (9 x + 25)

Factor out 9 x + 25 from the expression

(x - 20) (9 x + 25)

(x - 20) (9 x + 25) = 0

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

x - 20 = 0 9 x + 25 = 0

Solve the equation for x

More Steps

Evaluate

x - 20 = 0

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

x = 0 + 20

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

x = 20

x = 20 9 x + 25 = 0

Solve the equation for x

More Steps

Evaluate

9 x + 25 = 0

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

9 x = 0 - 25

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

9 x = - 25

Divide both sides

\frac{9 x}{9} = \frac{- 25}{9}

Divide the numbers

x = \frac{- 25}{9}

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

x = - \frac{25}{9}

x = 20 x = - \frac{25}{9}

Solution

x_{1} = - \frac{25}{9}, x_{2} = 20

Alternative Form

x_{1} = - 2. \dot{7}, x_{2} = 20

Show Solution