x2 actually has two square roots. One of them is indeed x. The other one is negative x.
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square root of (x2 + 1) = no simplification (square root of x2) + 1 = x + 1
The square root of x has two answers. It's either x (which is +x), or it's -x. If we take x times x, the answer is x2. If we take -x times -x, the answer is also x2.
x² = x+110 x²-x-110 = 0 x1= -(-1/2) - Square root of ((1/2)²+110) x1 = 0.5 - 10.5 x1 = - 10 x2 = -(-1/2) + Square root of ((1/2)²+110) x2 = 0.5 + 10.5 x2 = 11
x²-x-12=0 x1=-(-1/2) - Square root of ((-1/2)²+12) x1=0.5 - 3.5 x1=-3 x2=-(-1/2) + Square root of ((-1/2)²+12) x2=0.5 + 3.5 x2=4
x2 = 81 Square root both sides:- x = +/- 9