Question 367314
There are two ways to do this. Both methods involve setting each expression equal to zero.


Method 1: 


{{{2x^2+16x+9=0}}} Start with the given equation.



Notice that the quadratic {{{2x^2+16x+9}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=2}}}, {{{B=16}}}, and {{{C=9}}}



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



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



{{{x = (-(16) +- sqrt( (16)^2-4(2)(9) ))/(2(2))}}} Plug in  {{{A=2}}}, {{{B=16}}}, and {{{C=9}}}



{{{x = (-16 +- sqrt( 256-4(2)(9) ))/(2(2))}}} Square {{{16}}} to get {{{256}}}. 



{{{x = (-16 +- sqrt( 256-72 ))/(2(2))}}} Multiply {{{4(2)(9)}}} to get {{{72}}}



{{{x = (-16 +- sqrt( 184 ))/(2(2))}}} Subtract {{{72}}} from {{{256}}} to get {{{184}}}



{{{x = (-16 +- sqrt( 184 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (-16 +- 2*sqrt(46))/(4)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-16+2*sqrt(46))/(4)}}} or {{{x = (-16-2*sqrt(46))/(4)}}} Break up the expression.  



{{{x = (-8+sqrt(46))/(2)}}} or {{{x = (-8-sqrt(46))/(2)}}} Reduce.



So the solutions are {{{x = (-8+sqrt(46))/(2)}}} or {{{x = (-8-sqrt(46))/(2)}}} 



This means that the x-intercepts are *[Tex \LARGE \left(\frac{-8+\sqrt{46}}{2},0\right)] and *[Tex \LARGE \left(\frac{-8-\sqrt{46}}{2},0\right)]



======================================================================


Method 2: 



{{{2(x+4)^2-23=0}}} Start with the given equation.



{{{2(x+4)^2=0+23}}}Add {{{23}}} to both sides.



{{{2(x+4)^2=23}}} Combine like terms.



{{{(x+4)^2=(23)/(2)}}} Divide both sides by {{{2}}}.



{{{x+4=""+-sqrt(23/2)}}} Take the square root of both sides.



{{{x+4=sqrt(23/2)}}} or {{{x+4=-sqrt(23/2)}}} Break up the "plus/minus" to form two equations.



{{{x+4=sqrt(46)/2}}} or {{{x+4=-sqrt(46)/2}}}  Simplify the square root.



{{{x=-4+sqrt(46)/2}}} or {{{x=-4-sqrt(46)/2}}} Subtract {{{4}}} from both sides.



{{{x=(-8+sqrt(46))/(2)}}} or {{{x=(-8-sqrt(46))/(2)}}} Combine the fractions.



--------------------------------------



Answer:



So the solutions are {{{x=(-8+sqrt(46))/(2)}}} or {{{x=(-8-sqrt(46))/(2)}}}.



So again, the x-intercepts are *[Tex \LARGE \left(\frac{-8+\sqrt{46}}{2},0\right)] and *[Tex \LARGE \left(\frac{-8-\sqrt{46}}{2},0\right)]



Note: The approximate form of the x-intercepts is x-intercepts are *[Tex \LARGE \left(-0.608835,0\right)] and *[Tex \LARGE \left(-7.39116,0\right)]



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim