Solve 4x^2 - 12x - 7 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0.5, x_{2} = 3.5

Evaluate

4 x^{2} - 12 x - 7 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 12 x - 7

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out 2 x from the expression

2 x (2 x + 1) - 7 \times 2 x - 7

Factor out - 7 from the expression

2 x (2 x + 1) - 7 (2 x + 1)

Factor out 2 x + 1 from the expression

(2 x - 7) (2 x + 1)

(2 x - 7) (2 x + 1) = 0

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

2 x - 7 = 0 2 x + 1 = 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}

x = \frac{7}{2} 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

x = \frac{7}{2} x = - \frac{1}{2}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 3.5

Show Solution