SOLUTION: how do you solve this equation? 4x^2-6=10x

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Question 553123: how do you solve this equation?
4x^2-6=10x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-6=10x Start with the given equation.


4x%5E2-6-10x=0 Get every term to the left side.


4x%5E2-10x-6=0 Rearrange the terms.


Notice that the quadratic 4x%5E2-10x-6 is in the form of Ax%5E2%2BBx%2BC where A=4, B=-10, 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-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%284%29%28-6%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-10, and C=-6


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%284%29%28-6%29+%29%29%2F%282%284%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%284%29%28-6%29+%29%29%2F%282%284%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100--96+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-6%29 to get -96


x+=+%2810+%2B-+sqrt%28+100%2B96+%29%29%2F%282%284%29%29 Rewrite sqrt%28100--96%29 as sqrt%28100%2B96%29


x+=+%2810+%2B-+sqrt%28+196+%29%29%2F%282%284%29%29 Add 100 to 96 to get 196


x+=+%2810+%2B-+sqrt%28+196+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%2810+%2B-+14%29%2F%288%29 Take the square root of 196 to get 14.


x+=+%2810+%2B+14%29%2F%288%29 or x+=+%2810+-+14%29%2F%288%29 Break up the expression.


x+=+%2824%29%2F%288%29 or x+=++%28-4%29%2F%288%29 Combine like terms.


x+=+3 or x+=+-1%2F2 Simplify.


So the solutions are x+=+3 or x+=+-1%2F2


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