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

The answer to x^2+x+2sqrt(x^2+x-3)=3 is x\approx 1.30277…,x\approx-2.30277…

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

The solution is x\approx 1.30277…,x\approx-2.30277…

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x^{2} + x + 2 x^{2} + x - 3 = 3

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

Solution steps

x^{2} + x + 2 x^{2} + x - 3 = 3

Remove square roots

4 x^{2} + 4 x - 12 = x^{4} + 2 x^{3} - 5 x^{2} - 6 x + 9

Solve

4 x^{2} + 4 x - 12 = x^{4} + 2 x^{3} - 5 x^{2} - 6 x + 9 : x \approx 2.19258 \dots, x \approx 1.30277 \dots, x \approx - 2.30277 \dots, x \approx - 3.19258 \dots

x \approx 2.19258 \dots, x \approx 1.30277 \dots, x \approx - 2.30277 \dots, x \approx - 3.19258 \dots

Verify Solutions:

x \approx 2.19258 \dots

False

, x \approx 1.30277 \dots

True

, x \approx - 2.30277 \dots

True

, x \approx - 3.19258 \dots

False

The solutions are

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

2 n = 3 n - 1

5 x^{\frac{3}{2}} - 25 = 0

t^{\frac{1}{2}} = 3

x + a = a, a < 0

What is the answer to x^2+x+2sqrt(x^2+x-3)=3 ?
The answer to x^2+x+2sqrt(x^2+x-3)=3 is x\approx 1.30277…,x\approx-2.30277…
Solve for x: x^2+x+2sqrt(x^2+x-3)=3
The solution is x\approx 1.30277…,x\approx-2.30277…