SOLUTION: Solve for x:10^x to the power of 2 - x equals 100 Please show me steps to get the answer of x = -1 or 2

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Question 133263: Solve for x:10^x to the power of 2 - x equals 100
Please show me steps to get the answer of x = -1 or 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
10%5E%28x%5E2-x%29+=+100 Start with the given equation


10%5E%28x%5E2-x%29+=+10%5E2 Rewrite 100 as 10%5E2


Since the bases are equal, this means that the exponents are equal. So x%5E2-x=2


x%5E2-x=2 Set the exponents equal to one another


x%5E2-x-2=0 Subtract 2 from both sides.



%28x-2%29%28x%2B1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-2=0 or x%2B1=0

x=2 or x=-1 Now solve for x in each case


So our answer is
x=2 or x=-1