Solve 3x^2-27x=30

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 1, x_{2} = 10

Evaluate

3 x^{2} - 27 x = 30

Move the expression to the left side

3 x^{2} - 27 x - 30 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 27 x - 30

Rewrite the expression

3 x^{2} - 3 \times 9 x - 3 \times 10

Factor out 3 from the expression

3 (x^{2} - 9 x - 10)

Factor the expression

More Steps

Evaluate

x^{2} - 9 x - 10

Rewrite the expression

x^{2} + (1 - 10) x - 10

Calculate

x^{2} + x - 10 x - 10

Rewrite the expression

x \times x + x - 10 x - 10

Factor out x from the expression

x (x + 1) - 10 x - 10

Factor out - 10 from the expression

x (x + 1) - 10 (x + 1)

Factor out x + 1 from the expression

(x - 10) (x + 1)

3 (x - 10) (x + 1)

3 (x - 10) (x + 1) = 0

Divide the terms

(x - 10) (x + 1) = 0

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

x - 10 = 0 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 10 = 0

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

x = 0 + 10

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

x = 10

x = 10 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = 10 x = - 1

Solution

x_{1} = - 1, x_{2} = 10

Show Solution