Solve sqrt(x^(2)-4x 16)

Question

Simplify the expression

x^{2} - 64 x

Evaluate

x^{2} - 4 x \times 16

Solution

x^{2} - 64 x

Show Solution

x_{1} = 0, x_{2} = 64

Evaluate

x^{2} - 4 x \times 16

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

x^{2} - 4 x \times 16 = 0

Find the domain

More Steps

Evaluate

x^{2} - 4 x \times 16 \geq 0

Multiply the terms

x^{2} - 64 x \geq 0

Add the same value to both sides

x^{2} - 64 x + 1024 \geq 1024

Evaluate

(x - 32)^{2} \geq 1024

Take the 2 -th root on both sides of the inequality

(x - 32)^{2} \geq 1024

Calculate

∣ x - 32 ∣ \geq 32

Separate the inequality into 2 possible cases

x - 32 \geq 32 x - 32 \leq - 32

Calculate

More Steps

Evaluate

x - 32 \geq 32

Move the constant to the right side

x \geq 32 + 32

Add the numbers

x \geq 64

x \geq 64 x - 32 \leq - 32

Cancel equal terms on both sides of the expression

x \geq 64 x \leq 0

Find the union

x \in (- \infty, 0] \cup [64, + \infty)

x^{2} - 4 x \times 16 = 0, x \in (- \infty, 0] \cup [64, + \infty)

Calculate

x^{2} - 4 x \times 16 = 0

Multiply the terms

x^{2} - 64 x = 0

The only way a root could be 0 is when the radicand equals 0

x^{2} - 64 x = 0

Factor the expression

More Steps

Evaluate

x^{2} - 64 x

Rewrite the expression

x \times x - x \times 64

Factor out x from the expression

x (x - 64)

x (x - 64) = 0

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

x = 0 x - 64 = 0

Solve the equation for x

More Steps

Evaluate

x - 64 = 0

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

x = 0 + 64

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

x = 64

x = 0 x = 64

Check if the solution is in the defined range

x = 0 x = 64, x \in (- \infty, 0] \cup [64, + \infty)

Find the intersection of the solution and the defined range

x = 0 x = 64

Solution

x_{1} = 0, x_{2} = 64

Show Solution