What is the answer to x+sqrt(2x-1)=2(x-3)^2 ?

The answer to x+sqrt(2x-1)=2(x-3)^2 is x=5,x=(11-sqrt(17))/4

Solve for x: x+sqrt(2x-1)=2(x-3)^2

The solution is x=5,x=(11-sqrt(17))/4

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x + 2 x - 1 = 2 (x - 3)^{2}

x = 5, x = \frac{11 - 17}{4}

Decimal Notation

x = 5, x = 1.71922 \dots

Solution steps

x + 2 x - 1 = 2 (x - 3)^{2}

Expand

2 (x - 3)^{2} : 2 x^{2} - 12 x + 18

x + 2 x - 1 = 2 x^{2} - 12 x + 18

Remove square roots

2 x - 1 = 4 x^{4} - 52 x^{3} + 241 x^{2} - 468 x + 324

Solve

2 x - 1 = 4 x^{4} - 52 x^{3} + 241 x^{2} - 468 x + 324 : x = 5, x = \frac{5}{2}, x = \frac{11 + 17}{4}, x = \frac{11 - 17}{4}

x = 5, x = \frac{5}{2}, x = \frac{11 + 17}{4}, x = \frac{11 - 17}{4}

Verify Solutions:

x = 5

True

, x = \frac{5}{2}

False

, x = \frac{11 + 17}{4}

False

, x = \frac{11 - 17}{4}

True

The solutions are

x = 5, x = \frac{11 - 17}{4}

x 8 x + 1 = 5

x - 4 = 1

x + 1 + 9 x + 9 = 2 x + 2

x, x + 5 = x - 1

What is the answer to x+sqrt(2x-1)=2(x-3)^2 ?
The answer to x+sqrt(2x-1)=2(x-3)^2 is x=5,x=(11-sqrt(17))/4
Solve for x: x+sqrt(2x-1)=2(x-3)^2
The solution is x=5,x=(11-sqrt(17))/4