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

The answer to x^2-5=sqrt(x+5) is x\approx 2.79128…,x\approx-2.56155…

Solve for x: x^2-5=sqrt(x+5)

The solution is x\approx 2.79128…,x\approx-2.56155…

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x^{2} - 5 = x + 5

x \approx 2.79128 \dots, x \approx - 2.56155 \dots

Solution steps

x^{2} - 5 = x + 5

Square both sides:

x^{4} - 10 x^{2} + 25 = x + 5

x^{4} - 10 x^{2} + 25 = x + 5

Solve

x^{4} - 10 x^{2} + 25 = x + 5 : x \approx 2.79128 \dots, x \approx - 2.56155 \dots, x \approx 1.56155 \dots, x \approx - 1.79128 \dots

x \approx 2.79128 \dots, x \approx - 2.56155 \dots, x \approx 1.56155 \dots, x \approx - 1.79128 \dots

Verify Solutions:

x \approx 2.79128 \dots

True

, x \approx - 2.56155 \dots

True

, x \approx 1.56155 \dots

False

, x \approx - 1.79128 \dots

False

The solutions are

x \approx 2.79128 \dots, x \approx - 2.56155 \dots

x - 5 = 3 x - 11

x^{\frac{5}{6}} = 32

x + 3 + \frac{6}{x + 3} = 5

1 - \frac{5}{120 - x} = 0

What is the answer to x^2-5=sqrt(x+5) ?
The answer to x^2-5=sqrt(x+5) is x\approx 2.79128…,x\approx-2.56155…
Solve for x: x^2-5=sqrt(x+5)
The solution is x\approx 2.79128…,x\approx-2.56155…