Question 554913


{{{4x^2+4x+1=16}}} Start with the given equation.



{{{4x^2+4x+1-16=0}}} Get every term to the left side.



{{{4x^2+4x-15=0}}} Combine like terms.



Notice that the quadratic {{{4x^2+4x-15}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=4}}}, {{{B=4}}}, and {{{C=-15}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(4) +- sqrt( (4)^2-4(4)(-15) ))/(2(4))}}} Plug in  {{{A=4}}}, {{{B=4}}}, and {{{C=-15}}}



{{{x = (-4 +- sqrt( 16-4(4)(-15) ))/(2(4))}}} Square {{{4}}} to get {{{16}}}. 



{{{x = (-4 +- sqrt( 16--240 ))/(2(4))}}} Multiply {{{4(4)(-15)}}} to get {{{-240}}}



{{{x = (-4 +- sqrt( 16+240 ))/(2(4))}}} Rewrite {{{sqrt(16--240)}}} as {{{sqrt(16+240)}}}



{{{x = (-4 +- sqrt( 256 ))/(2(4))}}} Add {{{16}}} to {{{240}}} to get {{{256}}}



{{{x = (-4 +- sqrt( 256 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{x = (-4 +- 16)/(8)}}} Take the square root of {{{256}}} to get {{{16}}}. 



{{{x = (-4 + 16)/(8)}}} or {{{x = (-4 - 16)/(8)}}} Break up the expression. 



{{{x = (12)/(8)}}} or {{{x =  (-20)/(8)}}} Combine like terms. 



{{{x = 3/2}}} or {{{x = -5/2}}} Simplify. 



So the solutions are {{{x = 3/2}}} or {{{x = -5/2}}} 



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