SOLUTION: Solve this: {{{x^2=5(x+4)}}} please give me a step by step solution.

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Question 24019: Solve this: x%5E2=5%28x%2B4%29 please give me a step by step solution.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+=+5%28x%2B4%29 this is saying where does the straight line, y=5(x+4) cross (ie is EQUAL TO) the curve y = x%5E2. This is difficult to solve as it stands and you would have to plot it on a graph and then your answer may not be a precise answer depending upon how good you were are drawing curves etc.

However, combining the 2 equations into one is easy, as follows:
x%5E2+=+5%28x%2B4%29
x%5E2+=+5x%2B20
x%5E2+-+5x+-+20+=+0

Now we have one equation, y+=+x%5E2+-+5x+-+20 and we need to know where this crosses the x-axis, namely y=0. This is much better to solve, since we do not need to plot a graph. We can do it mathematically and arrive at the precise answer(s).

So... method is to factorise, hopefully. If not, then use the quadratic formula. I can see no obvious factorisation, so quadratic formula it is:

x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29
x+=+%28-%28-5%29+%2B-+sqrt%28%28-5%29%5E2-4%281%29%28-20%29%29%29%2F%282%281%29%29
x+=+%285+%2B-+sqrt%2825%2B80%29%29%2F2
x+=+%285+%2B-+sqrt%28105%29%29%2F2
x+=+%285+%2B+sqrt%28105%29%29%2F2 or x+=+%285+-+sqrt%28105%29%29%2F2

These are the 2 precise answers. You can use a calculator but you will have to round up the answers it gives you, thus being approximate answers.

jon.