Solve 2x^2 + 3x - 14 = 0

Question

Solve the quadratic equation

x_{1} = - \frac{7}{2}, x_{2} = 2

Alternative Form

x_{1} = - 3.5, x_{2} = 2

Evaluate

2 x^{2} + 3 x - 14 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 3 x - 14

Rewrite the expression

2 x^{2} + (7 - 4) x - 14

Calculate

2 x^{2} + 7 x - 4 x - 14

Rewrite the expression

x \times 2 x + x \times 7 - 2 \times 2 x - 2 \times 7

Factor out x from the expression

x (2 x + 7) - 2 \times 2 x - 2 \times 7

Factor out - 2 from the expression

x (2 x + 7) - 2 (2 x + 7)

Factor out 2 x + 7 from the expression

(x - 2) (2 x + 7)

(x - 2) (2 x + 7) = 0

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

x - 2 = 0 2 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 2 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 7 = 0

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

2 x = 0 - 7

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

2 x = - 7

Divide both sides

\frac{2 x}{2} = \frac{- 7}{2}

Divide the numbers

x = \frac{- 7}{2}

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

x = - \frac{7}{2}

x = 2 x = - \frac{7}{2}

Solution

x_{1} = - \frac{7}{2}, x_{2} = 2

Alternative Form

x_{1} = - 3.5, x_{2} = 2

Show Solution