Solve 28x^2-x-2=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{4}, x_{2} = \frac{2}{7}

Alternative Form

x_{1} = - 0.25, x_{2} = 0. \dot{2} 8571 \dot{4}

Evaluate

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

Factor the expression

More Steps

Evaluate

28 x^{2} - x - 2

Rewrite the expression

28 x^{2} + (- 8 + 7) x - 2

Calculate

28 x^{2} - 8 x + 7 x - 2

Rewrite the expression

4 x \times 7 x - 4 x \times 2 + 7 x - 2

Factor out 4 x from the expression

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

Factor out 7 x - 2 from the expression

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

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

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

7 x - 2 = 0 4 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

7 x - 2 = 0

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

7 x = 0 + 2

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

7 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{7}

x = \frac{2}{7} 4 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 1 = 0

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

4 x = 0 - 1

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

4 x = - 1

Divide both sides

\frac{4 x}{4} = \frac{- 1}{4}

Divide the numbers

x = \frac{- 1}{4}

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

x = - \frac{1}{4}

x = \frac{2}{7} x = - \frac{1}{4}

Solution

x_{1} = - \frac{1}{4}, x_{2} = \frac{2}{7}

Alternative Form

x_{1} = - 0.25, x_{2} = 0. \dot{2} 8571 \dot{4}

Show Solution