Question 169987


{{{x^2+4x-12}}} Start with the left side of the equation.



Take half of the {{{x}}} coefficient {{{4}}} to get {{{2}}}. In other words, {{{(1/2)(4)=2}}}.



Now square {{{2}}} to get {{{4}}}. In other words, {{{(2)^2=(2)(2)=4}}}



{{{x^2+4x+highlight(4-4)-12}}} Now add <font size=4><b>and</b></font> subtract {{{4}}}. Make sure to place this after the "x" term. Notice how {{{4-4=0}}}. So the expression is not changed.



{{{(x^2+4x+4)-4-12}}} Group the first three terms.



{{{(x+2)^2-4-12}}} Factor {{{x^2+4x+4}}} to get {{{(x+2)^2}}}.



{{{(x+2)^2-16}}} Combine like terms.



So after completing the square, {{{x^2+4x-12}}} transforms to {{{(x+2)^2-16}}}. So {{{x^2+4x-12=(x+2)^2-16}}}.



So {{{x^2+4x-12=0}}} is equivalent to {{{(x+2)^2-16=0}}}.



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{{{(x+2)^2-16=0}}} Start with the given equation.



{{{(x+2)^2=0+16}}}Add {{{16}}} to both sides.



{{{(x+2)^2=16}}} Combine like terms.



{{{x+2=0+-sqrt(16)}}} Take the square root of both sides.



{{{x+2=sqrt(16)}}} or {{{x+2=-sqrt(16)}}} Break up the "plus/minus" to form two equations.



{{{x+2=4}}} or {{{x+2=-4}}}  Take the square root of {{{16}}} to get {{{4}}}.



{{{x=-2+4}}} or {{{x=-2-4}}} Subtract {{{2}}} from both sides.



{{{x=2}}} or {{{x=-6}}} Combine like terms.



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Answer:



So the solutions are {{{x=2}}} or {{{x=-6}}}.