Download Completing squares in the equation 2x2 − 4x + 2y 2 + 2z2 + 20z = 1

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Completing squares in the equation 2x2 − 4x + 2y 2 + 2z 2 + 20z = 1 gives
2(x2 − 2x + 1) + 2y 2 + 2(z 2 + 10z + 25) = 1 + 2 + 50 ⇒
53
2(x − 1)2 + 2y 2 + 2(z + 5)2 = 53 ⇒ (x − 1)2 + y 2 + (z + 5)2 = , which
2
we recognize
r
√ as an equation of a sphere with center (1, 0, −5) and radius
53
106
=
.
2
2
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