SOLUTION: Not sure if I submitted my last question right. The problem is to solve the quadratic equation using the Indian method of multiplying each term in the equation by four times the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Not sure if I submitted my last question right. The problem is to solve the quadratic equation using the Indian method of multiplying each term in the equation by four times the      Log On


   

Question 148748: Not sure if I submitted my last question right.
The problem is to solve the quadratic equation using the Indian method of multiplying each term in the equation by four times the coefficient of the x sqrt 2 term.
The equation is 4x^2 - 4x + 3 = 0
Please help
Ellen
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+-+4x+%2B+3+=+0+ Start with the given equation.


x%5E2+-+x+%2B+3%2F4+=+0+ Divide everything by the leading coefficient 4. We must have a leading coefficient of 1.


x%5E2+-+x+=+-3%2F4+ Subtract 3%2F4 from both sides.


x%5E2+-+x+%2B1%2F4=+-3%2F4%2B1%2F4+ Take half of the x coefficient -1 and square it to get 1%2F4. Add this to both sides.


4x%5E2+-+4x+%2B1=+-3%2B1+ Multiply every term by 4. This will eliminate the denominators.



4x%5E2+-+4x%2B1+=+-2+ Combine like terms.


%282x-1%29%5E2+=+-2+ Factor 4x%5E2+-+4x%2B1 to get %282x-1%29%5E2.


2x-1+=+0%2B-sqrt%28-2%29+ Take the square root of both sides to eliminate the squares.


2x-1+=+sqrt%28-2%29+ or 2x-1+=+-sqrt%28-2%29+ Break up the expression.


2x-1+=+i%2Asqrt%282%29+ or 2x-1+=+-i%2Asqrt%282%29+ Simplify the square root.


2x=+1%2Bi%2Asqrt%282%29+ or 2x-1+=+1-i%2Asqrt%282%29+ Add 1 to both sides.


x=+%281%2Bi%2Asqrt%282%29%29%2F2+ or x=%281%2Bi%2Asqrt%282%29%29%2F2+ Divide both sides by 2 to isolate x.


So our answers are x=+%281%2Bi%2Asqrt%282%29%29%2F2+ or x=%281%2Bi%2Asqrt%282%29%29%2F2+


which approximate to x=1.207%2Ai or x=-0.207%2Ai