SOLUTION: Please help me solve this equation: {{{ 2x^2-86x=180 }}}.

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Question 334385: Please help me solve this equation: +2x%5E2-86x=180+.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-86x=180 Start with the given equation.


2x%5E2-86x-180=0 Subtract 180 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-86, and c=-180


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-%28-86%29+%2B-+sqrt%28+%28-86%29%5E2-4%282%29%28-180%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-86, and c=-180


x+=+%2886+%2B-+sqrt%28+%28-86%29%5E2-4%282%29%28-180%29+%29%29%2F%282%282%29%29 Negate -86 to get 86.


x+=+%2886+%2B-+sqrt%28+7396-4%282%29%28-180%29+%29%29%2F%282%282%29%29 Square -86 to get 7396.


x+=+%2886+%2B-+sqrt%28+7396--1440+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-180%29 to get -1440


x+=+%2886+%2B-+sqrt%28+7396%2B1440+%29%29%2F%282%282%29%29 Rewrite sqrt%287396--1440%29 as sqrt%287396%2B1440%29


x+=+%2886+%2B-+sqrt%28+8836+%29%29%2F%282%282%29%29 Add 7396 to 1440 to get 8836


x+=+%2886+%2B-+sqrt%28+8836+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%2886+%2B-+94%29%2F%284%29 Take the square root of 8836 to get 94.


x+=+%2886+%2B+94%29%2F%284%29 or x+=+%2886+-+94%29%2F%284%29 Break up the expression.


x+=+%28180%29%2F%284%29 or x+=++%28-8%29%2F%284%29 Combine like terms.


x+=+45 or x+=+-2 Simplify.


So the answers are x+=+45 or x+=+-2