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(a-b)^2 Expansion and Visualisation

Solve: x2+y2...

Question

Solve:
$x^{2} + y^{2} + z^{2} + 14 x - 14 z = 0$

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Solution

$x^{2} + y^{2} + z^{2} + 14 x - 14 z = 0$
$\Rightarrow x^{2} + 14 x + y^{2} + z^{2} - 14 z = 0$
$\Rightarrow x^{2} + 14 x + 49 - 49 + y^{2} + z^{2} - 14 z + 49 - 49 = 0$
$\Rightarrow {(x + 7)}^{2} + {(z - 7)}^{2} + y^{2} - 98 = 0$
This is possible if and only if each is equal to zero.
${(x + 7)}^{2} = 0$ and $y^{2} - 98 = 0$ and ${(z - 7)}^{2} = 0$
$\Rightarrow x = - 7$ ; $y = \pm 7 \sqrt{2}$ ; $z = 7$

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