Question 420024


{{{4x^2=14x+8}}} Start with the given equation.



{{{4x^2-14x-8=0}}} Get all terms to the left side.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=4}}}, {{{b=-14}}}, 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 = (-(-14) +- sqrt( (-14)^2-4(4)(-8) ))/(2(4))}}} Plug in  {{{a=4}}}, {{{b=-14}}}, and {{{c=-8}}}



{{{x = (14 +- sqrt( (-14)^2-4(4)(-8) ))/(2(4))}}} Negate {{{-14}}} to get {{{14}}}. 



{{{x = (14 +- sqrt( 196-4(4)(-8) ))/(2(4))}}} Square {{{-14}}} to get {{{196}}}. 



{{{x = (14 +- sqrt( 196--128 ))/(2(4))}}} Multiply {{{4(4)(-8)}}} to get {{{-128}}}



{{{x = (14 +- sqrt( 196+128 ))/(2(4))}}} Rewrite {{{sqrt(196--128)}}} as {{{sqrt(196+128)}}}



{{{x = (14 +- sqrt( 324 ))/(2(4))}}} Add {{{196}}} to {{{128}}} to get {{{324}}}



{{{x = (14 +- sqrt( 324 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{x = (14 +- 18)/(8)}}} Take the square root of {{{324}}} to get {{{18}}}. 



{{{x = (14 + 18)/(8)}}} or {{{x = (14 - 18)/(8)}}} Break up the expression. 



{{{x = (32)/(8)}}} or {{{x =  (-4)/(8)}}} Combine like terms. 



{{{x = 4}}} or {{{x = -1/2}}} Simplify. 



So the answers are {{{x = 4}}} or {{{x = -1/2}}} 

  


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