Solve (x-5)(x-1)-21=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 2, x_{2} = 8

Evaluate

(x - 5) (x - 1) - 21 = 0

Expand the expression

More Steps

Evaluate

(x - 5) (x - 1) - 21

Multiply the terms

More Steps

Evaluate

(x - 5) (x - 1)

Apply the distributive property

x \times x - x \times 1 - 5 x - (- 5 \times 1)

Multiply the terms

x^{2} - x \times 1 - 5 x - (- 5 \times 1)

Any expression multiplied by 1 remains the same

x^{2} - x - 5 x - (- 5 \times 1)

Any expression multiplied by 1 remains the same

x^{2} - x - 5 x - (- 5)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Subtract the terms

x^{2} - 6 x + 5

x^{2} - 6 x + 5 - 21

Subtract the numbers

x^{2} - 6 x - 16

x^{2} - 6 x - 16 = 0

Factor the expression

More Steps

Evaluate

x^{2} - 6 x - 16

Rewrite the expression

x^{2} + (2 - 8) x - 16

Calculate

x^{2} + 2 x - 8 x - 16

Rewrite the expression

x \times x + x \times 2 - 8 x - 8 \times 2

Factor out x from the expression

x (x + 2) - 8 x - 8 \times 2

Factor out - 8 from the expression

x (x + 2) - 8 (x + 2)

Factor out x + 2 from the expression

(x - 8) (x + 2)

(x - 8) (x + 2) = 0

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

x - 8 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 8 = 0

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

x = 0 + 8

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

x = 8

x = 8 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = 8 x = - 2

Solution

x_{1} = - 2, x_{2} = 8

Show Solution

Solve the quadratic equation

Graph