Solve 5x^2-12x-65=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{13}{5}, x_{2} = 5

Alternative Form

x_{1} = - 2.6, x_{2} = 5

Evaluate

5 x^{2} - 12 x - 65 = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 12 x - 65

Rewrite the expression

5 x^{2} + (13 - 25) x - 65

Calculate

5 x^{2} + 13 x - 25 x - 65

Rewrite the expression

x \times 5 x + x \times 13 - 5 \times 5 x - 5 \times 13

Factor out x from the expression

x (5 x + 13) - 5 \times 5 x - 5 \times 13

Factor out - 5 from the expression

x (5 x + 13) - 5 (5 x + 13)

Factor out 5 x + 13 from the expression

(x - 5) (5 x + 13)

(x - 5) (5 x + 13) = 0

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

x - 5 = 0 5 x + 13 = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 5 x + 13 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 13 = 0

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

5 x = 0 - 13

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

5 x = - 13

Divide both sides

\frac{5 x}{5} = \frac{- 13}{5}

Divide the numbers

x = \frac{- 13}{5}

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

x = - \frac{13}{5}

x = 5 x = - \frac{13}{5}

Solution

x_{1} = - \frac{13}{5}, x_{2} = 5

Alternative Form

x_{1} = - 2.6, x_{2} = 5

Show Solution