Solve 63x^2 - 32x - 63 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{7}{9}, x_{2} = \frac{9}{7}

Alternative Form

x_{1} = - 0. \dot{7}, x_{2} = 1. \dot{2} 8571 \dot{4}

Evaluate

63 x^{2} - 32 x - 63 = 0

Factor the expression

More Steps

Evaluate

63 x^{2} - 32 x - 63

Rewrite the expression

63 x^{2} + (49 - 81) x - 63

Calculate

63 x^{2} + 49 x - 81 x - 63

Rewrite the expression

7 x \times 9 x + 7 x \times 7 - 9 \times 9 x - 9 \times 7

Factor out 7 x from the expression

7 x (9 x + 7) - 9 \times 9 x - 9 \times 7

Factor out - 9 from the expression

7 x (9 x + 7) - 9 (9 x + 7)

Factor out 9 x + 7 from the expression

(7 x - 9) (9 x + 7)

(7 x - 9) (9 x + 7) = 0

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

7 x - 9 = 0 9 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

7 x - 9 = 0

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

7 x = 0 + 9

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

7 x = 9

Divide both sides

\frac{7 x}{7} = \frac{9}{7}

Divide the numbers

x = \frac{9}{7}

x = \frac{9}{7} 9 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

9 x + 7 = 0

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

9 x = 0 - 7

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

9 x = - 7

Divide both sides

\frac{9 x}{9} = \frac{- 7}{9}

Divide the numbers

x = \frac{- 7}{9}

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

x = - \frac{7}{9}

x = \frac{9}{7} x = - \frac{7}{9}

Solution

x_{1} = - \frac{7}{9}, x_{2} = \frac{9}{7}

Alternative Form

x_{1} = - 0. \dot{7}, x_{2} = 1. \dot{2} 8571 \dot{4}

Show Solution