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

The answer to 4-x^2=sqrt(2-x) is x=2,x\approx 1.93543…,x\approx-1.46259…

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

The solution is x=2,x\approx 1.93543…,x\approx-1.46259…

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4 - x^{2} = 2 - x

x = 2, x \approx 1.93543 \dots, x \approx - 1.46259 \dots

Solution steps

4 - x^{2} = 2 - x

Square both sides:

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

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

Solve

16 - 8 x^{2} + x^{4} = 2 - x : x = 2, x \approx 1.93543 \dots, x \approx - 1.46259 \dots, x \approx - 2.47283 \dots

x = 2, x \approx 1.93543 \dots, x \approx - 1.46259 \dots, x \approx - 2.47283 \dots

Verify Solutions:

x = 2

True

, x \approx 1.93543 \dots

True

, x \approx - 1.46259 \dots

True

, x \approx - 2.47283 \dots

False

The solutions are

x = 2, x \approx 1.93543 \dots, x \approx - 1.46259 \dots

2 x - 4 = 10

6 w + 13 = 8 w + 3

x^{\frac{1}{2}} + 2 = 0

27 - 3 x = x + 9

4 x - 64 = 6

What is the answer to 4-x^2=sqrt(2-x) ?
The answer to 4-x^2=sqrt(2-x) is x=2,x\approx 1.93543…,x\approx-1.46259…
Solve for x: 4-x^2=sqrt(2-x)
The solution is x=2,x\approx 1.93543…,x\approx-1.46259…