What is the answer to solvefor x,sqrt(x)+k=x ?

The answer to solvefor x,sqrt(x)+k=x is x=(2k+1+sqrt(4k+1))/2 ,x=(2k+1-sqrt(4k+1))/2

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solvefor x,sqrt(x)+k=x

x, x + k = x

x = \frac{2 k + 1 + 4 k + 1}{2}, x = \frac{2 k + 1 - 4 k + 1}{2}

Solution steps

x + k = x

Remove square roots

x = x^{2} - 2 k x + k^{2}

Solve

x = x^{2} - 2 k x + k^{2} : x = \frac{2 k + 1 + 4 k + 1}{2}, x = \frac{2 k + 1 - 4 k + 1}{2}

x = \frac{2 k + 1 + 4 k + 1}{2}, x = \frac{2 k + 1 - 4 k + 1}{2}

Verify Solutions:

x = \frac{2 k + 1 + 4 k + 1}{2}

True

, x = \frac{2 k + 1 - 4 k + 1}{2}

True

The solutions are

x = \frac{2 k + 1 + 4 k + 1}{2}, x = \frac{2 k + 1 - 4 k + 1}{2}

4 a^{2} - 4 a + 1 + a + 4 = a + 7

8 4 z^{2} - 43 = 40

x + 8 - x^{2} = 0

x + 1 = x + 1

What is the answer to solvefor x,sqrt(x)+k=x ?
The answer to solvefor x,sqrt(x)+k=x is x=(2k+1+sqrt(4k+1))/2 ,x=(2k+1-sqrt(4k+1))/2