SOLUTION: solve 5x^2-x-6=0 rearange into standard form 2x-3=x^2

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Question 323283: solve 5x^2-x-6=0
rearange into standard form
2x-3=x^2
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve 5x^-x-6=0
Is it 5x%5E%28-x-6%29+=+0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



5x%5E2-x-6=0 Start with the given equation.


Notice that the quadratic 5x%5E2-x-6 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-1, and C=-6


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%285%29%28-6%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-1, and C=-6


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%285%29%28-6%29+%29%29%2F%282%285%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%285%29%28-6%29+%29%29%2F%282%285%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--120+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-6%29 to get -120


x+=+%281+%2B-+sqrt%28+1%2B120+%29%29%2F%282%285%29%29 Rewrite sqrt%281--120%29 as sqrt%281%2B120%29


x+=+%281+%2B-+sqrt%28+121+%29%29%2F%282%285%29%29 Add 1 to 120 to get 121


x+=+%281+%2B-+sqrt%28+121+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%281+%2B-+11%29%2F%2810%29 Take the square root of 121 to get 11.


x+=+%281+%2B+11%29%2F%2810%29 or x+=+%281+-+11%29%2F%2810%29 Break up the expression.


x+=+%2812%29%2F%2810%29 or x+=++%28-10%29%2F%2810%29 Combine like terms.


x+=+6%2F5 or x+=+-1 Simplify.


So the solutions are x+=+6%2F5 or x+=+-1

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# 2


2x-3=x%5E2 Start with the given equation.


-3=x%5E2-2x Subtract 2x from both sides.


0=x%5E2-2x%2B3 Add 3 to both sides.


x%5E2-2x%2B3=0 Rearrange the equation.


Now the equation is in standard form Ax%5E2%2BBx%2BC=0