Solve 2x^2-13x-45=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{5}{2}, x_{2} = 9

Alternative Form

x_{1} = - 2.5, x_{2} = 9

Evaluate

2 x^{2} - 13 x - 45 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 13 x - 45

Rewrite the expression

2 x^{2} + (5 - 18) x - 45

Calculate

2 x^{2} + 5 x - 18 x - 45

Rewrite the expression

x \times 2 x + x \times 5 - 9 \times 2 x - 9 \times 5

Factor out x from the expression

x (2 x + 5) - 9 \times 2 x - 9 \times 5

Factor out - 9 from the expression

x (2 x + 5) - 9 (2 x + 5)

Factor out 2 x + 5 from the expression

(x - 9) (2 x + 5)

(x - 9) (2 x + 5) = 0

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

x - 9 = 0 2 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 9 = 0

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

x = 0 + 9

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

x = 9

x = 9 2 x + 5 = 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}

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

x = - \frac{5}{2}

x = 9 x = - \frac{5}{2}

Solution

x_{1} = - \frac{5}{2}, x_{2} = 9

Alternative Form

x_{1} = - 2.5, x_{2} = 9

Show Solution