Questions on Algebra: Quadratic Equation answered by real tutors!

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> Questions on Algebra: Quadratic Equation answered by real tutors!     (Log On)
Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!

   

Question 151432: Will the quadratic equation work on an equation such as x^2 - 3=0? : Will the quadratic equation work on an equation such as x^2 - 3=0?
Answer by jim_thompson5910(9217) About Me  (Show Source):
You can put this solution on YOUR website!

x^2-3=0 Start with the given equation.


Take note that x^2-3=0 really looks like x^2+0x+(-3)=0


Notice we have a quadratic equation in the form of ax^2+bx+c where a=1, b=0, 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 = (-(0) +- sqrt( (0)^2-4(1)(-3) ))/(2(1)) Plug in a=1, b=0, and c=-3


x = (-0 +- sqrt( 0-4(1)(-3) ))/(2(1)) Square 0 to get 0.


x = (-0 +- sqrt( 0--12 ))/(2(1)) Multiply 4(1)(-3) to get -12


x = (-0 +- sqrt( 0+12 ))/(2(1)) Rewrite sqrt(0--12) as sqrt(0+12)


x = (-0 +- sqrt( 12 ))/(2(1)) Add 0 to 12 to get 12


x = (-0 +- sqrt( 12 ))/(2) Multiply 2 and 1 to get 2.


x = (-0 +- 2*sqrt(3))/(2) Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x = (-0)/(2) +- (2*sqrt(3))/(2) Break up the fraction.


x = 0 +- sqrt(3) Reduce.


x = sqrt(3) or x = -sqrt(3) Break up the expression.


So our answers are x = sqrt(3) or x = -sqrt(3)


which approximate to x=1.732 or x=-1.732


Note: even though the quadratic formula works perfectly here, there is a much faster way to solve this problem.