Sqrt[x^2-5]+Sqrt[x^2+7]=15-x^2

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Solution for Sqrt[x^2-5]+Sqrt[x^2+7]=15-x^2 equation:


Simplifying
Sqrt[x2 + -5] + Sqrt[x2 + 7] = 15 + -1x2

Reorder the terms:
qrtS[-5 + x2] + Sqrt[x2 + 7] = 15 + -1x2
[-5 * qrtS + x2 * qrtS] + Sqrt[x2 + 7] = 15 + -1x2
[-5qrtS + qrtx2S] + Sqrt[x2 + 7] = 15 + -1x2

Reorder the terms:
-5qrtS + qrtx2S + qrtS[7 + x2] = 15 + -1x2
-5qrtS + qrtx2S + [7 * qrtS + x2 * qrtS] = 15 + -1x2
-5qrtS + qrtx2S + [7qrtS + qrtx2S] = 15 + -1x2

Reorder the terms:
-5qrtS + 7qrtS + qrtx2S + qrtx2S = 15 + -1x2

Combine like terms: -5qrtS + 7qrtS = 2qrtS
2qrtS + qrtx2S + qrtx2S = 15 + -1x2

Combine like terms: qrtx2S + qrtx2S = 2qrtx2S
2qrtS + 2qrtx2S = 15 + -1x2

Solving
2qrtS + 2qrtx2S = 15 + -1x2

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Reorder the terms:
-15 + 2qrtS + 2qrtx2S + x2 = 15 + -1x2 + -15 + x2

Reorder the terms:
-15 + 2qrtS + 2qrtx2S + x2 = 15 + -15 + -1x2 + x2

Combine like terms: 15 + -15 = 0
-15 + 2qrtS + 2qrtx2S + x2 = 0 + -1x2 + x2
-15 + 2qrtS + 2qrtx2S + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-15 + 2qrtS + 2qrtx2S + x2 = 0

The solution to this equation could not be determined.

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