What is the answer to x+sqrt(7-\sqrt{x)}=11 ?

The answer to x+sqrt(7-\sqrt{x)}=11 is x=9

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x+sqrt(7-\sqrt{x)}=11

x + 7 - x = 11

x = 9

Solution steps

x + 7 - x = 11

Remove square roots

x = x^{4} - 44 x^{3} + 712 x^{2} - 5016 x + 12996

Solve

x = x^{4} - 44 x^{3} + 712 x^{2} - 5016 x + 12996 : x = 9, x \approx 7.86868 \dots, x \approx 12.84812 \dots, x \approx 14.28318 \dots

x = 9, x \approx 7.86868 \dots, x \approx 12.84812 \dots, x \approx 14.28318 \dots

Verify Solutions:

x = 9

True

, x \approx 7.86868 \dots

False

, x \approx 12.84812 \dots

False

, x \approx 14.28318 \dots

False

The solution is

x = 9

2 x + 5 = 2 x + 1

2 x - 3 - x = 2 x - 6

x 4 - x^{2} = 0

4 - x^{2} = 1

What is the answer to x+sqrt(7-\sqrt{x)}=11 ?
The answer to x+sqrt(7-\sqrt{x)}=11 is x=9
Solve for x: x+sqrt(7-\sqrt{x)}=11
The solution is x=9