What is the answer to x^2+6x+sqrt(x^2+6x+8)=64 ?

The answer to x^2+6x+sqrt(x^2+6x+8)=64 is x\approx 5.06225…,x\approx-11.06225…

Solve for x: x^2+6x+sqrt(x^2+6x+8)=64

The solution is x\approx 5.06225…,x\approx-11.06225…

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x^{2} + 6 x + x^{2} + 6 x + 8 = 64

x \approx 5.06225 \dots, x \approx - 11.06225 \dots

Solution steps

x^{2} + 6 x + x^{2} + 6 x + 8 = 64

Remove square roots

x^{2} + 6 x + 8 = x^{4} + 12 x^{3} - 92 x^{2} - 768 x + 4096

Solve

x^{2} + 6 x + 8 = x^{4} + 12 x^{3} - 92 x^{2} - 768 x + 4096 : x \approx 5.06225 \dots, x \approx - 11.06225 \dots, x \approx 6.05538 \dots, x \approx - 12.05538 \dots

x \approx 5.06225 \dots, x \approx - 11.06225 \dots, x \approx 6.05538 \dots, x \approx - 12.05538 \dots

Verify Solutions:

x \approx 5.06225 \dots

True

, x \approx - 11.06225 \dots

True

, x \approx 6.05538 \dots

False

, x \approx - 12.05538 \dots

False

The solutions are

x \approx 5.06225 \dots, x \approx - 11.06225 \dots

5 x + 4 = 4 + x + 4

x + 2 = x + 10

3 x - 2 - x + 3 = 1

x + 5 - 1 = x - 2

x + \frac{4}{x} = 5

What is the answer to x^2+6x+sqrt(x^2+6x+8)=64 ?
The answer to x^2+6x+sqrt(x^2+6x+8)=64 is x\approx 5.06225…,x\approx-11.06225…
Solve for x: x^2+6x+sqrt(x^2+6x+8)=64
The solution is x\approx 5.06225…,x\approx-11.06225…