Solve -3x^2-35x-189=13x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Evaluate

- 3 x^{2} - 35 x - 189 = 13 x

Move the expression to the left side

- 3 x^{2} - 48 x - 189 = 0

Factor the expression

More Steps

Evaluate

- 3 x^{2} - 48 x - 189

Rewrite the expression

- 3 x^{2} - 3 \times 16 x - 3 \times 63

Factor out - 3 from the expression

- 3 (x^{2} + 16 x + 63)

Factor the expression

More Steps

Evaluate

x^{2} + 16 x + 63

Rewrite the expression

x^{2} + (9 + 7) x + 63

Calculate

x^{2} + 9 x + 7 x + 63

Rewrite the expression

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

Factor out x from the expression

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

Factor out 7 from the expression

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

Factor out x + 9 from the expression

(x + 7) (x + 9)

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

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

Divide the terms

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

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

x + 7 = 0 x + 9 = 0

Solve the equation for x

More Steps

Evaluate

x + 7 = 0

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

x = 0 - 7

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

x = - 7

x = - 7 x + 9 = 0

Solve the equation for x

More Steps

Evaluate

x + 9 = 0

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

x = 0 - 9

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

x = - 9

x = - 7 x = - 9

Solution

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

Show Solution