SOLUTION: x^2+8x+144=16/9

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Question 201591: x^2+8x+144=16/9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B8x%2B144=16%2F9 Start with the given equation.


9%2Ax%5E2%2B9%2A8x%2B9%2A144=cross%289%29%2A%2816%2Fcross%289%29%29 Multiply EVERY term by the LCD 9 to clear out the fraction.


9x%5E2%2B72x%2B1296=16 Multiply and simplify


9x%5E2%2B72x%2B1296-16=0 Subtract 16 from both sides.


9x%5E2%2B72x%2B1280=0 Combine like terms.


Notice that the quadratic 9x%5E2%2B72x%2B1280 is in the form of Ax%5E2%2BBx%2BC where A=9, B=72, and C=1280


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-%2872%29+%2B-+sqrt%28+%2872%29%5E2-4%289%29%281280%29+%29%29%2F%282%289%29%29 Plug in A=9, B=72, and C=1280


x+=+%28-72+%2B-+sqrt%28+5184-4%289%29%281280%29+%29%29%2F%282%289%29%29 Square 72 to get 5184.


x+=+%28-72+%2B-+sqrt%28+5184-46080+%29%29%2F%282%289%29%29 Multiply 4%289%29%281280%29 to get 46080


x+=+%28-72+%2B-+sqrt%28+-40896+%29%29%2F%282%289%29%29 Subtract 46080 from 5184 to get -40896


x+=+%28-72+%2B-+sqrt%28+-40896+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28-72+%2B-+24i%2Asqrt%2871%29%29%2F%2818%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-72%2B24i%2Asqrt%2871%29%29%2F%2818%29 or x+=+%28-72-24i%2Asqrt%2871%29%29%2F%2818%29 Break up the expression.


So the solutions are x+=+%28-72%2B24i%2Asqrt%2871%29%29%2F%2818%29 or x+=+%28-72-24i%2Asqrt%2871%29%29%2F%2818%29