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

The answer to x^2-4=sqrt(x+4) is x\approx 2.56155…,x\approx-2.30277…

Solve for x: x^2-4=sqrt(x+4)

The solution is x\approx 2.56155…,x\approx-2.30277…

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x^{2} - 4 = x + 4

x \approx 2.56155 \dots, x \approx - 2.30277 \dots

Solution steps

x^{2} - 4 = x + 4

Square both sides:

x^{4} - 8 x^{2} + 16 = x + 4

x^{4} - 8 x^{2} + 16 = x + 4

Solve

x^{4} - 8 x^{2} + 16 = x + 4 : x \approx 2.56155 \dots, x \approx - 2.30277 \dots, x \approx 1.30277 \dots, x \approx - 1.56155 \dots

x \approx 2.56155 \dots, x \approx - 2.30277 \dots, x \approx 1.30277 \dots, x \approx - 1.56155 \dots

Verify Solutions:

x \approx 2.56155 \dots

True

, x \approx - 2.30277 \dots

True

, x \approx 1.30277 \dots

False

, x \approx - 1.56155 \dots

False

The solutions are

x \approx 2.56155 \dots, x \approx - 2.30277 \dots

2 x - 1 + 5 = 2

x + 4 = 2 x - 1

4 x + 44 + 2 = 10

\frac{1 - x}{2} = x

What is the answer to x^2-4=sqrt(x+4) ?
The answer to x^2-4=sqrt(x+4) is x\approx 2.56155…,x\approx-2.30277…
Solve for x: x^2-4=sqrt(x+4)
The solution is x\approx 2.56155…,x\approx-2.30277…