Solve (2x-4)(x)=160

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 8, x_{2} = 10

Evaluate

(2 x - 4) x = 160

Multiply the terms

x (2 x - 4) = 160

Expand the expression

More Steps

Evaluate

x (2 x - 4)

Apply the distributive property

x \times 2 x - x \times 4

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} - x \times 4

Use the commutative property to reorder the terms

2 x^{2} - 4 x

2 x^{2} - 4 x = 160

Move the expression to the left side

2 x^{2} - 4 x - 160 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 4 x - 160

Rewrite the expression

2 x^{2} - 2 \times 2 x - 2 \times 80

Factor out 2 from the expression

2 (x^{2} - 2 x - 80)

Factor the expression

More Steps

Evaluate

x^{2} - 2 x - 80

Rewrite the expression

x^{2} + (8 - 10) x - 80

Calculate

x^{2} + 8 x - 10 x - 80

Rewrite the expression

x \times x + x \times 8 - 10 x - 10 \times 8

Factor out x from the expression

x (x + 8) - 10 x - 10 \times 8

Factor out - 10 from the expression

x (x + 8) - 10 (x + 8)

Factor out x + 8 from the expression

(x - 10) (x + 8)

2 (x - 10) (x + 8)

2 (x - 10) (x + 8) = 0

Divide the terms

(x - 10) (x + 8) = 0

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

x - 10 = 0 x + 8 = 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 + 8 = 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 = 10 x = - 8

Solution

x_{1} = - 8, x_{2} = 10

Show Solution