Solve 7x^(2)-132x-667=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{29}{7}, x_{2} = 23

Alternative Form

x_{1} = - 4. \dot{1} 4285 \dot{7}, x_{2} = 23

Evaluate

7 x^{2} - 132 x - 667 = 0

Factor the expression

More Steps

Evaluate

7 x^{2} - 132 x - 667

Rewrite the expression

7 x^{2} + (29 - 161) x - 667

Calculate

7 x^{2} + 29 x - 161 x - 667

Rewrite the expression

x \times 7 x + x \times 29 - 23 \times 7 x - 23 \times 29

Factor out x from the expression

x (7 x + 29) - 23 \times 7 x - 23 \times 29

Factor out - 23 from the expression

x (7 x + 29) - 23 (7 x + 29)

Factor out 7 x + 29 from the expression

(x - 23) (7 x + 29)

(x - 23) (7 x + 29) = 0

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

x - 23 = 0 7 x + 29 = 0

Solve the equation for x

More Steps

Evaluate

x - 23 = 0

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

x = 0 + 23

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

x = 23

x = 23 7 x + 29 = 0

Solve the equation for x

More Steps

Evaluate

7 x + 29 = 0

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

7 x = 0 - 29

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

7 x = - 29

Divide both sides

\frac{7 x}{7} = \frac{- 29}{7}

Divide the numbers

x = \frac{- 29}{7}

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

x = - \frac{29}{7}

x = 23 x = - \frac{29}{7}

Solution

x_{1} = - \frac{29}{7}, x_{2} = 23

Alternative Form

x_{1} = - 4. \dot{1} 4285 \dot{7}, x_{2} = 23

Show Solution