Question

What value is the positive solution of 5= 8 + 2x - x²

Answer 1

The answer is 3

So, because there is an $x^{2}$ in this equation, that means there will be two solutions for x. To find these solutions, let's solve for x:

5 - 8 - 2x + $x^{2}$ = 0..................................Move all terms to one side

-2x + $x^{2}$ -3 = 0.......................................Combine like terms (5 -8 = -3)

(x - 3) (x + 1)............................................Factor -2x + $x^{2}$ -3 = 0

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How to Factor:
-2x + $x^{2}$ -3 = 0

Ask which two numbers add up to equal -2 and multiply to equal -3
(-3 and 1)

Not just put the in a parenthesis with an x in front: (x - 3) (x + 1)

To check this multiply the parenthesis together by using the FOIL method and you will end up with -2x + $x^{2}$ -3 = 0 which is exactly what we started with.
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Now that that is factored, all we do now is set each parenthesis to equal 0 and solve for x:

x - 3 = 0
x = 3

x + 1 =0
x = -1

Now our question asks us for the positive solution, which is 3.

Thank you for the question! I hope this helped!! Have an amazing day! :)