Question 211327
# 10




{{{x^2+4x+3=0}}} Start with the given equation.



Notice that the quadratic {{{x^2+4x+3}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=4}}}, and {{{C=3}}}



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(1)(3) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=4}}}, and {{{C=3}}}



{{{x = (-4 +- sqrt( 16-4(1)(3) ))/(2(1))}}} Square {{{4}}} to get {{{16}}}. 



{{{x = (-4 +- sqrt( 16-12 ))/(2(1))}}} Multiply {{{4(1)(3)}}} to get {{{12}}}



{{{x = (-4 +- sqrt( 4 ))/(2(1))}}} Subtract {{{12}}} from {{{16}}} to get {{{4}}}



{{{x = (-4 +- sqrt( 4 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-4 +- 2)/(2)}}} Take the square root of {{{4}}} to get {{{2}}}. 



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



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



{{{x = -1}}} or {{{x = -3}}} Simplify. 



So the solutions are {{{x = -1}}} or {{{x = -3}}} 

  

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# 42



{{{9m^2+16=24m}}} Start with the given equation.



{{{9m^2+16-24m=0}}} Subtract 24m from both sides.



{{{9m^2-24m+16=0}}} Rearrange the terms.



From {{{9m^2-24m+16}}} we can see that {{{a=9}}}, {{{b=-24}}}, and {{{c=16}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(-24)^2-4(9)(16)}}} Plug in {{{a=9}}}, {{{b=-24}}}, and {{{c=16}}}



{{{D=576-4(9)(16)}}} Square {{{-24}}} to get {{{576}}}



{{{D=576-576}}} Multiply {{{4(9)(16)}}} to get {{{(36)(16)=576}}}



{{{D=0}}} Subtract {{{576}}} from {{{576}}} to get {{{0}}}



Since the discriminant is equal to zero, this means that there is one real solution.