Question 195102
3)


{{{x^2-20x}}} Start with the given expression



Now take half of the x coefficient and square it to get {{{(-20/2)^2=(-10)^2=100}}}. This is the value that you add to the expression to make it a perfect square.


So {{{x^2-20x+100}}} is a perfect square.



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4)


Is the equation {{{x^2+8x+8=0}}} ???




{{{x^2+8x+8=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=8}}}, and {{{c=8}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(8) +- sqrt( (8)^2-4(1)(8) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=8}}}, and {{{c=8}}}



{{{x = (-8 +- sqrt( 64-4(1)(8) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64-32 ))/(2(1))}}} Multiply {{{4(1)(8)}}} to get {{{32}}}



{{{x = (-8 +- sqrt( 32 ))/(2(1))}}} Subtract {{{32}}} from {{{64}}} to get {{{32}}}



{{{x = (-8 +- sqrt( 32 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-8 +- 4*sqrt(2))/(2)}}} Simplify the square root 



{{{x = (-8)/(2) +- (4*sqrt(2))/(2)}}} Break up the fraction.  



{{{x = -4 +- 2*sqrt(2)}}} Reduce.  



{{{x = -4+2*sqrt(2)}}} or {{{x = -4-2*sqrt(2)}}} Break up the expression.  



So the answers are {{{x = -4+2*sqrt(2)}}} or {{{x = -4-2*sqrt(2)}}} 



which approximate to {{{x=-1.172}}} or {{{x=-6.828}}} 



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OR....


Is the equation {{{x^2+8x-8=0}}} ???





{{{x^2+8x-8=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=8}}}, and {{{c=-8}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(8) +- sqrt( (8)^2-4(1)(-8) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=8}}}, and {{{c=-8}}}



{{{x = (-8 +- sqrt( 64-4(1)(-8) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64--32 ))/(2(1))}}} Multiply {{{4(1)(-8)}}} to get {{{-32}}}



{{{x = (-8 +- sqrt( 64+32 ))/(2(1))}}} Rewrite {{{sqrt(64--32)}}} as {{{sqrt(64+32)}}}



{{{x = (-8 +- sqrt( 96 ))/(2(1))}}} Add {{{64}}} to {{{32}}} to get {{{96}}}



{{{x = (-8 +- sqrt( 96 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-8 +- 4*sqrt(6))/(2)}}} Simplify the square root 



{{{x = (-8)/(2) +- (4*sqrt(6))/(2)}}} Break up the fraction.  



{{{x = -4 +- 2*sqrt(6)}}} Reduce.  



{{{x = -4+2*sqrt(6)}}} or {{{x = -4-2*sqrt(6)}}} Break up the expression.  



So the answers are {{{x = -4+2*sqrt(6)}}} or {{{x = -4-2*sqrt(6)}}} 



which approximate to {{{x=0.899}}} or {{{x=-8.899}}}