Solve 9x^2-20x-21 = 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} = 3

Alternative Form

x_{1} = - 0. \dot{7}, x_{2} = 3

Evaluate

9 x^{2} - 20 x - 21 = 0

Factor the expression

More Steps

Evaluate

9 x^{2} - 20 x - 21

Rewrite the expression

9 x^{2} + (7 - 27) x - 21

Calculate

9 x^{2} + 7 x - 27 x - 21

Rewrite the expression

x \times 9 x + x \times 7 - 3 \times 9 x - 3 \times 7

Factor out x from the expression

x (9 x + 7) - 3 \times 9 x - 3 \times 7

Factor out - 3 from the expression

x (9 x + 7) - 3 (9 x + 7)

Factor out 9 x + 7 from the expression

(x - 3) (9 x + 7)

(x - 3) (9 x + 7) = 0

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

x - 3 = 0 9 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 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 = 3 x = - \frac{7}{9}

Solution

x_{1} = - \frac{7}{9}, x_{2} = 3

Alternative Form

x_{1} = - 0. \dot{7}, x_{2} = 3

Show Solution