Solve 15x^2 - 224x - 15 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{15}, x_{2} = 15

Alternative Form

x_{1} = - 0.0 \dot{6}, x_{2} = 15

Evaluate

15 x^{2} - 224 x - 15 = 0

Factor the expression

More Steps

Evaluate

15 x^{2} - 224 x - 15

Rewrite the expression

15 x^{2} + (1 - 225) x - 15

Calculate

15 x^{2} + x - 225 x - 15

Rewrite the expression

x \times 15 x + x - 15 \times 15 x - 15

Factor out x from the expression

x (15 x + 1) - 15 \times 15 x - 15

Factor out - 15 from the expression

x (15 x + 1) - 15 (15 x + 1)

Factor out 15 x + 1 from the expression

(x - 15) (15 x + 1)

(x - 15) (15 x + 1) = 0

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

x - 15 = 0 15 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 15 = 0

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

x = 0 + 15

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

x = 15

x = 15 15 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

15 x + 1 = 0

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

15 x = 0 - 1

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

15 x = - 1

Divide both sides

\frac{15 x}{15} = \frac{- 1}{15}

Divide the numbers

x = \frac{- 1}{15}

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

x = - \frac{1}{15}

x = 15 x = - \frac{1}{15}

Solution

x_{1} = - \frac{1}{15}, x_{2} = 15

Alternative Form

x_{1} = - 0.0 \dot{6}, x_{2} = 15

Show Solution