Question 276999


{{{5x^2-10x-2}}} Start with the given expression.



{{{5(x^2-2x-2/5)}}} Factor out the {{{x^2}}} coefficient {{{5}}}. This step is very important: the {{{x^2}}} coefficient <font size=4><b>must</b></font> be equal to 1.



Take half of the {{{x}}} coefficient {{{-2}}} to get {{{-1}}}. In other words, {{{(1/2)(-2)=-1}}}.



Now square {{{-1}}} to get {{{1}}}. In other words, {{{(-1)^2=(-1)(-1)=1}}}



{{{5(x^2-2x+highlight(1-1)-2/5)}}} Now add <font size=4><b>and</b></font> subtract {{{1}}} inside the parenthesis. Make sure to place this after the "x" term. Notice how {{{1-1=0}}}. So the expression is not changed.



{{{5((x^2-2x+1)-1-2/5)}}} Group the first three terms.



{{{5((x-1)^2-1-2/5)}}} Factor {{{x^2-2x+1}}} to get {{{(x-1)^2}}}.



{{{5((x-1)^2-7/5)}}} Combine like terms.



{{{5(x-1)^2+5(-7/5)}}} Distribute.



{{{5(x-1)^2-7}}} Multiply.



So after completing the square, {{{5x^2-10x-2}}} transforms to {{{5(x-1)^2-7}}}. So {{{5x^2-10x-2=5(x-1)^2-7}}}.