SOLUTION: I need help solving this equation: {{{u^2-8=7u}}}

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Question 227735: I need help solving this equation: u%5E2-8=7u
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

u%5E2-8=7u Start with the given equation.


u%5E2-7u-8=0 Subtract 7u from both sides.


Notice that the quadratic u%5E2-7u-8 is in the form of Au%5E2%2BBu%2BC where A=1, B=-7, and C=-8


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


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


u+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-7, and C=-8


u+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


u+=+%287+%2B-+sqrt%28+49-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


u+=+%287+%2B-+sqrt%28+49--32+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-8%29 to get -32


u+=+%287+%2B-+sqrt%28+49%2B32+%29%29%2F%282%281%29%29 Rewrite sqrt%2849--32%29 as sqrt%2849%2B32%29


u+=+%287+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 49 to 32 to get 81


u+=+%287+%2B-+sqrt%28+81+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


u+=+%287+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


u+=+%287+%2B+9%29%2F%282%29 or u+=+%287+-+9%29%2F%282%29 Break up the expression.


u+=+%2816%29%2F%282%29 or u+=++%28-2%29%2F%282%29 Combine like terms.


u+=+8 or u+=+-1 Simplify.


So the solutions are u+=+8 or u+=+-1