What is the answer to sqrt(4x^2-12x+9)=3-2x ?

The answer to sqrt(4x^2-12x+9)=3-2x is x<= 3/2

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sqrt(4x^2-12x+9)=3-2x

4 x^{2} - 12 x + 9 = 3 - 2 x

x \leq \frac{3}{2}

Solution steps

4 x^{2} - 12 x + 9 = 3 - 2 x

Square both sides:

4 x^{2} - 12 x + 9 = 9 - 12 x + 4 x^{2}

4 x^{2} - 12 x + 9 = 9 - 12 x + 4 x^{2}

Solve

4 x^{2} - 12 x + 9 = 9 - 12 x + 4 x^{2} :

True for all

x

True for all x

Verify Solutions:

x < \frac{3}{2}

True

, x = \frac{3}{2}

True

, x > \frac{3}{2}

False

The solution is

x \leq \frac{3}{2}

x + 7 = 6 + 4 x

2 x = 4 x^{2} - 5 x + 50

3 (x + 2)^{\frac{3}{2}} = 24

3 t + 7 = - 5

2 x^{- 1} - 5 x^{- \frac{1}{2}} + 3 = 0

What is the answer to sqrt(4x^2-12x+9)=3-2x ?
The answer to sqrt(4x^2-12x+9)=3-2x is x<= 3/2
Solve for x: sqrt(4x^2-12x+9)=3-2x
The solution is x<= 3/2