SOLUTION: Please help me solve this equation to find the value of x: x^2+5x-46=0 I have already done this: x2+5x=46

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Question 745448: Please help me solve this equation to find the value of x: x^2+5x-46=0
I have already done this: x2+5x=46
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
That step might be useful if you know how or are trying to complete the square. First, look at what is simpler. Can you factor x^2+5x-46 ? No. Nothing useful comes from +/- 23 or 2.

Next is to either directly use the general solution to the quadratic formula, or to Complete The Square to solve for the variable. This is where you got stuck with:
x%5E2%2B5x-46=0+
x%5E2%2B5x=46

The lefthand member is the same as x*(x+5). That is like a rectangle with one side of length x and the other side of length x+5. This rectangle contains a main square of length x, and an extra rectangular part of length 5 and height x. There is a graphical rearrangement that can be made, which I will not provide here and will not try to describe... but what you will do to perform the symbolic process of "completing the square" is, add %285%2F2%29%5E2 to both sides of the equation. %285%2F2%29%5E2=25%2F4.

x%5E2%2B5x%2B+25%2F4=46%2B25%2F4
The left side is now a square trinomial, and the righthand member is a sum of constants which can be calculated or computed.
Continuing,...

%28x%2B5%2F2%29%5E2=46%2A4%2F4%2B25%2F4
%28x%2B5%2F2%29%5E2=209%2F4
**x%2B5%2F2=0%2B-+sqrt%28209%2F4%29
x=-5%2F2%2B-+sqrt%28209%2F4%29
highlight%28x=-%285%2F2%29%2B-+sqrt%28209%29%2F2%29


**The extra 0 was added to the righthand member because without it, the rendering was given a messier wording included with the arrangement of symbols, making visual reading more difficult.