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

The answer to sqrt(4-x)=4-x^2 is x\approx-1.30277…,x\approx 1.56155…

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

The solution is x\approx-1.30277…,x\approx 1.56155…

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4 - x = 4 - x^{2}

x \approx - 1.30277 \dots, x \approx 1.56155 \dots

Solution steps

4 - x = 4 - x^{2}

Square both sides:

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

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

Solve

4 - x = 16 - 8 x^{2} + x^{4} : x \approx - 2.56155 \dots, x \approx 2.30277 \dots, x \approx - 1.30277 \dots, x \approx 1.56155 \dots

x \approx - 2.56155 \dots, x \approx 2.30277 \dots, x \approx - 1.30277 \dots, x \approx 1.56155 \dots

Verify Solutions:

x \approx - 2.56155 \dots

False

, x \approx 2.30277 \dots

False

, x \approx - 1.30277 \dots

True

, x \approx 1.56155 \dots

True

The solutions are

x \approx - 1.30277 \dots, x \approx 1.56155 \dots

2 x = 4 x^{2} + 6 x - 12

3 = 2 x^{2} - 17 x

5 x^{2} + 3 x - 11 = 4 x - 7

16 - x^{2} + x^{2} = 0

(x - 3)^{2} + (- 1 - 2)^{2} = 4

What is the answer to sqrt(4-x)=4-x^2 ?
The answer to sqrt(4-x)=4-x^2 is x\approx-1.30277…,x\approx 1.56155…
Solve for x: sqrt(4-x)=4-x^2
The solution is x\approx-1.30277…,x\approx 1.56155…