Solve 2x^2-7x-39=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 3, x_{2} = \frac{13}{2}

Alternative Form

x_{1} = - 3, x_{2} = 6.5

Evaluate

2 x^{2} - 7 x - 39 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 7 x - 39

Rewrite the expression

2 x^{2} + (- 13 + 6) x - 39

Calculate

2 x^{2} - 13 x + 6 x - 39

Rewrite the expression

x \times 2 x - x \times 13 + 3 \times 2 x - 3 \times 13

Factor out x from the expression

x (2 x - 13) + 3 \times 2 x - 3 \times 13

Factor out 3 from the expression

x (2 x - 13) + 3 (2 x - 13)

Factor out 2 x - 13 from the expression

(x + 3) (2 x - 13)

(x + 3) (2 x - 13) = 0

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

2 x - 13 = 0 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 13 = 0

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

2 x = 0 + 13

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

2 x = 13

Divide both sides

\frac{2 x}{2} = \frac{13}{2}

Divide the numbers

x = \frac{13}{2}

x = \frac{13}{2} x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x + 3 = 0

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

x = 0 - 3

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

x = - 3

x = \frac{13}{2} x = - 3

Solution

x_{1} = - 3, x_{2} = \frac{13}{2}

Alternative Form

x_{1} = - 3, x_{2} = 6.5

Show Solution