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

The answer to x^2-5=sqrt(x+2) is x\approx 2.67627…

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x^2-5=sqrt(x+2)

x^{2} - 5 = x + 2

x \approx 2.67627 \dots

Solution steps

x^{2} - 5 = x + 2

Square both sides:

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

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

Solve

x^{4} - 10 x^{2} + 25 = x + 2 : x \approx 2.67627 \dots, x \approx 1.75026 \dots

x \approx 2.67627 \dots, x \approx 1.75026 \dots

Verify Solutions:

x \approx 2.67627 \dots

True

, x \approx 1.75026 \dots

False

The solution is

x \approx 2.67627 \dots

x^{\frac{2}{3}} - 2 x^{\frac{1}{3}} - 8 = 0

x^{2} + 5 x - 10 = 0

x + 2 x - 1 = 2

16 + x + 18 = 121

- 9 x + 10 = 3 x^{0.2}

What is the answer to x^2-5=sqrt(x+2) ?
The answer to x^2-5=sqrt(x+2) is x\approx 2.67627…
Solve for x: x^2-5=sqrt(x+2)
The solution is x\approx 2.67627…