Solve x^2 -11x+30

Question

Factor the expression

(x - 6) (x - 5)

Evaluate

x^{2} - 11 x + 30

Rewrite the expression

x^{2} + (- 5 - 6) x + 30

Calculate

x^{2} - 5 x - 6 x + 30

Rewrite the expression

x \times x - x \times 5 - 6 x + 6 \times 5

Factor out x from the expression

x (x - 5) - 6 x + 6 \times 5

Factor out - 6 from the expression

x (x - 5) - 6 (x - 5)

Solution

(x - 6) (x - 5)

Show Solution

x_{1} = 5, x_{2} = 6

Evaluate

x^{2} - 11 x + 30

To find the roots of the expression,set the expression equal to 0

x^{2} - 11 x + 30 = 0

Factor the expression

More Steps

Evaluate

x^{2} - 11 x + 30

Rewrite the expression

x^{2} + (- 5 - 6) x + 30

Calculate

x^{2} - 5 x - 6 x + 30

Rewrite the expression

x \times x - x \times 5 - 6 x + 6 \times 5

Factor out x from the expression

x (x - 5) - 6 x + 6 \times 5

Factor out - 6 from the expression

x (x - 5) - 6 (x - 5)

Factor out x - 5 from the expression

(x - 6) (x - 5)

(x - 6) (x - 5) = 0

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

x - 6 = 0 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 6 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 6 x = 5

Solution

x_{1} = 5, x_{2} = 6

Show Solution