Solve 21x^2 -8x-4=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0. \dot{2} 8571 \dot{4}, x_{2} = 0. \dot{6}

Evaluate

21 x^{2} - 8 x - 4 = 0

Factor the expression

More Steps

Evaluate

21 x^{2} - 8 x - 4

Rewrite the expression

21 x^{2} + (6 - 14) x - 4

Calculate

21 x^{2} + 6 x - 14 x - 4

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out - 2 from the expression

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

Factor out 7 x + 2 from the expression

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

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

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

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

Solve the equation for x

More Steps

Evaluate

3 x - 2 = 0

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

3 x = 0 + 2

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

3 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{3}

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

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

x = - \frac{2}{7}

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

Solution

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

Alternative Form

x_{1} = - 0. \dot{2} 8571 \dot{4}, x_{2} = 0. \dot{6}

Show Solution