SOLUTION: Can you Please help me with this problem. x2-2x-13=0 (x2, the x is squared, can't find the key to square it,)

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Question 200192This question is from textbook Mathematics in Our World
: Can you Please help me with this problem.
x2-2x-13=0
(x2, the x is squared, can't find the key to square it,)
 This question is from textbook Mathematics in Our World

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: to type x%5E2, just type in x^2


x%5E2-2x-13=0 Start with the given equation.


Notice that the quadratic x%5E2-2x-13 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=-13


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-13%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-13


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-13%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-13%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--52+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-13%29 to get -52


x+=+%282+%2B-+sqrt%28+4%2B52+%29%29%2F%282%281%29%29 Rewrite sqrt%284--52%29 as sqrt%284%2B52%29


x+=+%282+%2B-+sqrt%28+56+%29%29%2F%282%281%29%29 Add 4 to 52 to get 56


x+=+%282+%2B-+sqrt%28+56+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+2%2Asqrt%2814%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%2814%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+sqrt%2814%29 Reduce.


x+=+1%2Bsqrt%2814%29 or x+=+1-sqrt%2814%29 Break up the expression.


So the solutions are x+=+1%2Bsqrt%2814%29 or x+=+1-sqrt%2814%29


which approximate to x=4.742 or x=-2.742