SOLUTION: Can you please help me solve this equation {{{4x^2-4x+3=0}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can you please help me solve this equation {{{4x^2-4x+3=0}}}      Log On


   

Question 200195This question is from textbook Mathematics in our World
: Can you please help me solve this equation
4x%5E2-4x%2B3=0 This question is from textbook Mathematics in our World

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-4x%2B3=0 Start with the given equation.


Notice that the quadratic 4x%5E2-4x%2B3 is in the form of Ax%5E2%2BBx%2BC where A=4, B=-4, and C=3


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-4, and C=3


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%284%29%283%29+%29%29%2F%282%284%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-48+%29%29%2F%282%284%29%29 Multiply 4%284%29%283%29 to get 48


x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%282%284%29%29 Subtract 48 from 16 to get -32


x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%284+%2B-+4i%2Asqrt%282%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%284%2B4i%2Asqrt%282%29%29%2F%288%29 or x+=+%284-4i%2Asqrt%282%29%29%2F%288%29 Break up the expression.


x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29 or x+=+%281-i%2Asqrt%282%29%29%2F%282%29 Reduce


So the solutions are x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29 or x+=+%281-i%2Asqrt%282%29%29%2F%282%29