SOLUTION: Can you help me with this problem? 2(a-6)^2-45=53

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Question 408793: Can you help me with this problem? 2(a-6)^2-45=53
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%28a-6%29%5E2-45=53+ Start with the given equation.


2%28a%5E2-12a%2B36%29-45=53+ FOIL


2a%5E2-24a%2B72-45=53+ Distribute.


2a%5E2-24a%2B72-45-53=0+ Subtract 53 from both sides.


2a%5E2-24a-26=0+ Combine like terms.


Notice we have a quadratic equation in the form of Aa%5E2%2BBa%2BC where A=2, B=-24, and C=-26


Let's use the quadratic formula to solve for a


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


a+=+%28-%28-24%29+%2B-+sqrt%28+%28-24%29%5E2-4%282%29%28-26%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-24, and C=-26


a+=+%2824+%2B-+sqrt%28+%28-24%29%5E2-4%282%29%28-26%29+%29%29%2F%282%282%29%29 Negate -24 to get 24.


a+=+%2824+%2B-+sqrt%28+576-4%282%29%28-26%29+%29%29%2F%282%282%29%29 Square -24 to get 576.


a+=+%2824+%2B-+sqrt%28+576--208+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-26%29 to get -208


a+=+%2824+%2B-+sqrt%28+576%2B208+%29%29%2F%282%282%29%29 Rewrite sqrt%28576--208%29 as sqrt%28576%2B208%29


a+=+%2824+%2B-+sqrt%28+784+%29%29%2F%282%282%29%29 Add 576 to 208 to get 784


a+=+%2824+%2B-+sqrt%28+784+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


a+=+%2824+%2B-+28%29%2F%284%29 Take the square root of 784 to get 28.


a+=+%2824+%2B+28%29%2F%284%29 or a+=+%2824+-+28%29%2F%284%29 Break up the expression.


a+=+%2852%29%2F%284%29 or a+=++%28-4%29%2F%284%29 Combine like terms.


a+=+13 or a+=+-1 Simplify.


So the answers are a+=+13 or a+=+-1


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