Solve |x^2| |x-5| |x|

Question

Simplify the expression

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

Evaluate

x^{2} ∣ x - 5 ∣ ∣ x ∣

When the expression in absolute value bars is not negative, remove the bars

x^{2} ∣ x - 5 ∣ ∣ x ∣

Multiply the terms

x^{2} ∣ x ∣ ∣ x - 5 ∣

Multiply the terms

x^{2} ∣ x (x - 5) ∣

Solution

More Steps

Evaluate

x (x - 5)

Apply the distributive property

x \times x - x \times 5

Multiply the terms

x^{2} - x \times 5

Use the commutative property to reorder the terms

x^{2} - 5 x

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

Show Solution

x_{1} = 0, x_{2} = 5

Evaluate

x^{2} ∣ x - 5 ∣ ∣ x ∣

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

x^{2} ∣ x - 5 ∣ ∣ x ∣ = 0

When the expression in absolute value bars is not negative, remove the bars

x^{2} ∣ x - 5 ∣ ∣ x ∣ = 0

Multiply the terms

More Steps

Multiply the terms

x^{2} ∣ x - 5 ∣ ∣ x ∣

Multiply the terms

x^{2} ∣ x ∣ ∣ x - 5 ∣

Multiply the terms

x^{2} ∣ x (x - 5) ∣

x^{2} ∣ x (x - 5) ∣ = 0

Separate the equation into 2 possible cases

x^{2} = 0 ∣ x (x - 5) ∣ = 0

The only way a power can be 0 is when the base equals 0

x = 0 ∣ x (x - 5) ∣ = 0

Solve the equation

More Steps

Evaluate

∣ x (x - 5) ∣ = 0

Rewrite the expression

x (x - 5) = 0

Separate the equation into 2 possible cases

x = 0 x - 5 = 0

Solve the equation

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 = 0 x = 5

x = 0 x = 0 x = 5

Find the union

x = 0 x = 5

Solution

x_{1} = 0, x_{2} = 5

Show Solution