2 answers

Solve using the quadratic formula

Question:

Solve using the quadratic formula.
5x^2-2x-3=0

Answers

Ok, remember that the quadratic formula is (-b+-sqrt(b^2 -4ac))/2a : so (2+-sqrt(4+60))/10. So that equals (2+-8)/10.  So you have two answers (2+8)/10 or (2-8)/10. 1 or -6/10.

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{{{5x^2-3x-3=0}}} Start with the given equation. Notice that the quadratic {{{5x^2-3x-3}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=5}}}, {{{B=-3}}}, 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 = (-(-3) +- sqrt( (-3)^2-4(5)(-3) ))/(2(5))}}} Plug in {{{A=5}}}, {{{B=-3}}}, and {{{C=-3}}} {{{x = (3 +- sqrt( (-3)^2-4(5)(-3) ))/(2(5))}}} Negate {{{-3}}} to get {{{3}}}. {{{x = (3 +- sqrt( 9-4(5)(-3) ))/(2(5))}}} Square {{{-3}}} to get {{{9}}}. {{{x = (3 +- sqrt( 9--60 ))/(2(5))}}} Multiply {{{4(5)(-3)}}} to get {{{-60}}} {{{x = (3 +- sqrt( 9+60 ))/(2(5))}}} Rewrite {{{sqrt(9--60)}}} as {{{sqrt(9+60)}}} {{{x = (3 +- sqrt( 69 ))/(2(5))}}} Add {{{9}}} to {{{60}}} to get {{{69}}} {{{x = (3 +- sqrt( 69 ))/(10)}}} Multiply {{{2}}} and {{{5}}} to get {{{10}}}. {{{x = (3+sqrt(69))/(10)}}} or {{{x = (3-sqrt(69))/(10)}}} Break up the expression.

So the solutions are {{{x = (3+sqrt(69))/(10)}}} or {{{x = (3-sqrt(69))/(10)}}} which approximate to {{{x=1.131}}} or {{{x=-0.531}}}

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