What the answer to this equation be? ( (1)/(2) x) ^(2) - 3x = 7x + 8 - 10x ​

Question

What the answer to this equation be?


`( (1)/(2) x) ^(2) - 3x = 7x + 8 - 10x`
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Answer 1

If you expand the square, you have

`(1)/(4)x^2-3x=7x+8-10x`

Simplify the right hand side:

`(1)/(4)x^2-3x=-3x+8`

Cancel the -3x appearing on both sides:

`(1)/(4)x^2=8`

Multiply both sides by 4:

`x^2=32`

Consider the square root of both terms (using the doubles sign):

`x=\pm√(32)=\pm4√(2)`