What is the answer to |2x-5|^2-8|2x-5|+16=0 ?

The answer to |2x-5|^2-8|2x-5|+16=0 is x= 1/2 ,x= 9/2

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|2x-5|^2-8|2x-5|+16=0

∣ 2 x - 5 ∣^{2} - 8 ∣ 2 x - 5 ∣ + 16 = 0

x = \frac{1}{2}, x = \frac{9}{2}

Decimal Notation

x = 0.5, x = 4.5

Solution steps

∣ 2 x - 5 ∣^{2} - 8 ∣ 2 x - 5 ∣ + 16 = 0

Factor

∣ 2 x - 5 ∣^{2} - 8 ∣ 2 x - 5 ∣ + 16 : (∣ 2 x - 5 ∣ - 4)^{2}

(∣ 2 x - 5 ∣ - 4)^{2} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

∣ 2 x - 5 ∣ - 4 = 0

Solve

∣ 2 x - 5 ∣ - 4 = 0 : x = \frac{1}{2} or x = \frac{9}{2}

The solutions are

x = \frac{1}{2}, x = \frac{9}{2}

\frac{x}{2 x - 1} < x

5 + 4 (x - 1) = 2 x - 9

x - 5 > 4 x + 8 - 4

2 (f + 3) - 2 = 8 + 2 f

\frac{9}{5} = \frac{z}{20}

What is the answer to |2x-5|^2-8|2x-5|+16=0 ?
The answer to |2x-5|^2-8|2x-5|+16=0 is x= 1/2 ,x= 9/2
Solve for x: |2x-5|^2-8|2x-5|+16=0
The solution is x= 1/2 ,x= 9/2