SOLUTION: √(x+10)=2-x and √(x+3)=(x-1)/3 Full step-by-step instructions please

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Question 731801: √(x+10)=2-x
and
√(x+3)=(x-1)/3
Full step-by-step instructions please

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B10%29=2-x
Square both sides and simplify. Simplify means get all terms on one side and just 0 on the other side, and make terms in the order of general form, decreasing degree of x.

Those instructions might be a little too brief, so here is a refinement:
The right hand member contains a variable and a constant term. The left hand member uses the variable term and a constant term both inside the square root function. We want to unwrap the left hand member, so we start by squaring BOTH sides.

(1) Square both sides.
%28sqrt%28x%2B10%29%29%5E2=%282-x%29%5E2
x%2B10=4-4x%2Bx%5E2


(2) Use inverse operations to collect the terms to one side and have zero on the other side; we can detect by visual inspection that we'll have a quadratic equation.
x%5E2-4x%2B4=x%2B10
x%5E2-5x-6=0


(3) If you are interested in solving for x, you'd either use factoring or general solution to quadratic equation.
See if the quadratic expression is easy to factor first...
?*?=-6, ?+?=-5
-6*1=-6, -6+1=-5, that is the pair of constants for the linear binomials.
x%5E2-5x-6=%28x-6%29%28x%2B1%29=0