What is the answer to x^2+(-x/(x+2))^2=20 ?

The answer to x^2+(-x/(x+2))^2=20 is x=-4,x\approx-1.61322…,x\approx-2.80560…,x\approx 4.41883…

Solve for x: x^2+(-x/(x+2))^2=20

The solution is x=-4,x\approx-1.61322…,x\approx-2.80560…,x\approx 4.41883…

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x^{2} + (- \frac{x}{x + 2})^{2} = 20

x = - 4, x \approx - 1.61322 \dots, x \approx - 2.80560 \dots, x \approx 4.41883 \dots

Solution steps

x^{2} + (- \frac{x}{x + 2})^{2} = 20

Simplify

(- \frac{x}{x + 2})^{2} : \frac{x ^{2}}{( x + 2 ) ^{2}}

x^{2} + \frac{x ^{2}}{( x + 2 ) ^{2}} = 20

Multiply both sides by

(x + 2)^{2}

x^{2} (x + 2)^{2} + x^{2} = 20 (x + 2)^{2}

Solve

x^{2} (x + 2)^{2} + x^{2} = 20 (x + 2)^{2} : x = - 4, x \approx - 1.61322 \dots, x \approx - 2.80560 \dots, x \approx 4.41883 \dots

x = - 4, x \approx - 1.61322 \dots, x \approx - 2.80560 \dots, x \approx 4.41883 \dots

Verify Solutions

Find undefined (singularity) points:

x = - 2

Combine undefined points with solutions:

x = - 4, x \approx - 1.61322 \dots, x \approx - 2.80560 \dots, x \approx 4.41883 \dots

x - \frac{2}{x - 6} = \frac{5}{x - 6}

3 - \frac{3}{x - 9} = \frac{x}{x - 9}

\frac{1}{x} - \frac{2 x}{1 - x} = 1

\frac{2}{3} - \frac{1}{5} = \frac{7}{3 x}

\frac{3}{y} + 2 = \frac{7}{2 y}

What is the answer to x^2+(-x/(x+2))^2=20 ?
The answer to x^2+(-x/(x+2))^2=20 is x=-4,x\approx-1.61322…,x\approx-2.80560…,x\approx 4.41883…
Solve for x: x^2+(-x/(x+2))^2=20
The solution is x=-4,x\approx-1.61322…,x\approx-2.80560…,x\approx 4.41883…