The opposite of -36 is equal to 36
She made the mistake in step 4
She should have divided by -2 not just 2 alone
4x^2-3x+4y^2+4z^2=0
here we shall proceed as follows:
x=ρcosθsinφ
y=ρsinθsinφ
z=ρcosφ
thus
4x^2-3x+4y^2+4z^2=
4(ρcosθsinφ)^2-3(ρcosθsinφ)+4(ρsinθsinφ)^2+4(ρcosφ)
but
ρ=1/4cosθsinφ
hence we shall have:
4x^2-3x+4y^2+4z^2
=1/4cosθsinθ(cosθ(4-3sinφ))+4sin^2(φ)
Assuming that the side of the triangle marked 13.5 is tangent to the circle, the there's a right angle where the radius meets the tangent segment. The triangle is then a right triangle and the Pythagorean Theorem applies.
