```Question 395305

{{{2x^2-4-7x=0}}} Subtract 7x from both sides.

{{{2x^2-7x-4=0}}} Rearrange the terms.

Notice that the quadratic {{{2x^2-7x-4}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=2}}}, {{{B=-7}}}, and {{{C=-4}}}

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

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

{{{x = (-(-7) +- sqrt( (-7)^2-4(2)(-4) ))/(2(2))}}} Plug in  {{{A=2}}}, {{{B=-7}}}, and {{{C=-4}}}

{{{x = (7 +- sqrt( (-7)^2-4(2)(-4) ))/(2(2))}}} Negate {{{-7}}} to get {{{7}}}.

{{{x = (7 +- sqrt( 49-4(2)(-4) ))/(2(2))}}} Square {{{-7}}} to get {{{49}}}.

{{{x = (7 +- sqrt( 49--32 ))/(2(2))}}} Multiply {{{4(2)(-4)}}} to get {{{-32}}}

{{{x = (7 +- sqrt( 49+32 ))/(2(2))}}} Rewrite {{{sqrt(49--32)}}} as {{{sqrt(49+32)}}}

{{{x = (7 +- sqrt( 81 ))/(2(2))}}} Add {{{49}}} to {{{32}}} to get {{{81}}}

{{{x = (7 +- sqrt( 81 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}.

{{{x = (7 +- 9)/(4)}}} Take the square root of {{{81}}} to get {{{9}}}.

{{{x = (7 + 9)/(4)}}} or {{{x = (7 - 9)/(4)}}} Break up the expression.

{{{x = (16)/(4)}}} or {{{x =  (-2)/(4)}}} Combine like terms.

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

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

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```