Solve 6x^2 -2x-28=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 2, x_{2} = \frac{7}{3}

Alternative Form

x_{1} = - 2, x_{2} = 2. \dot{3}

Evaluate

6 x^{2} - 2 x - 28 = 0

Factor the expression

More Steps

Evaluate

6 x^{2} - 2 x - 28

Rewrite the expression

2 \times 3 x^{2} - 2 x - 2 \times 14

Factor out 2 from the expression

2 (3 x^{2} - x - 14)

Factor the expression

More Steps

Evaluate

3 x^{2} - x - 14

Rewrite the expression

3 x^{2} + (- 7 + 6) x - 14

Calculate

3 x^{2} - 7 x + 6 x - 14

Rewrite the expression

x \times 3 x - x \times 7 + 2 \times 3 x - 2 \times 7

Factor out x from the expression

x (3 x - 7) + 2 \times 3 x - 2 \times 7

Factor out 2 from the expression

x (3 x - 7) + 2 (3 x - 7)

Factor out 3 x - 7 from the expression

(x + 2) (3 x - 7)

2 (x + 2) (3 x - 7)

2 (x + 2) (3 x - 7) = 0

Divide the terms

(x + 2) (3 x - 7) = 0

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

3 x - 7 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 7 = 0

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

3 x = 0 + 7

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

3 x = 7

Divide both sides

\frac{3 x}{3} = \frac{7}{3}

Divide the numbers

x = \frac{7}{3}

x = \frac{7}{3} x + 2 = 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 = \frac{7}{3} x = - 2

Solution

x_{1} = - 2, x_{2} = \frac{7}{3}

Alternative Form

x_{1} = - 2, x_{2} = 2. \dot{3}

Show Solution