What is the answer to sqrt(4x^2-20x+25)=5-2x ?

The answer to sqrt(4x^2-20x+25)=5-2x is x<= 5/2

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sqrt(4x^2-20x+25)=5-2x

4 x^{2} - 20 x + 25 = 5 - 2 x

x \leq \frac{5}{2}

Solution steps

4 x^{2} - 20 x + 25 = 5 - 2 x

Square both sides:

4 x^{2} - 20 x + 25 = 25 - 20 x + 4 x^{2}

4 x^{2} - 20 x + 25 = 25 - 20 x + 4 x^{2}

Solve

4 x^{2} - 20 x + 25 = 25 - 20 x + 4 x^{2} :

True for all

x

True for all x

Verify Solutions:

x < \frac{5}{2}

True

, x = \frac{5}{2}

True

, x > \frac{5}{2}

False

The solution is

x \leq \frac{5}{2}

x + 1 = 3 + 2 x - 1

2 x - 5 = x - 4

x + 14 = x - 6

5 = x + 3

x + x^{\frac{1}{2}} - 6 = 0

What is the answer to sqrt(4x^2-20x+25)=5-2x ?
The answer to sqrt(4x^2-20x+25)=5-2x is x<= 5/2
Solve for x: sqrt(4x^2-20x+25)=5-2x
The solution is x<= 5/2