Question

What the answer to this equation be?

$( \frac{1}{2} x) ^{2} - 3x = 7x + 8 - 10x$
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Answer 1

If you expand the square, you have

$\dfrac{1}{4}x^2-3x=7x+8-10x$

Simplify the right hand side:

$\dfrac{1}{4}x^2-3x=-3x+8$

Cancel the -3x appearing on both sides:

$\dfrac{1}{4}x^2=8$

Multiply both sides by 4:

$x^2=32$

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

$x=\pm\sqrt{32}=\pm4\sqrt{2}$