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Solve 4x^2+2x-3=0 by completing the square
- Thread starter dkarolasz
- Start date
4x^2+2x-3 = 0
divide out by 4
x^2 + (1/2)x - (3/4) = 0
x^2 + (1/2)x = (3/4)
add ((1/2)b)^2 to both sides
x^2 + (1/2)x + (1/16) = (3/4) + (1/16)
simplify the right hand side, convert the left hand side to squared form
(x + (1/4))^2 = (13/16)
square root both sides
x + (1/4) = sqrt(13/16)
thus x = -(1/4) +/- sqrt(13/16)
See?
John.
divide out by 4
x^2 + (1/2)x - (3/4) = 0
x^2 + (1/2)x = (3/4)
add ((1/2)b)^2 to both sides
x^2 + (1/2)x + (1/16) = (3/4) + (1/16)
simplify the right hand side, convert the left hand side to squared form
(x + (1/4))^2 = (13/16)
square root both sides
x + (1/4) = sqrt(13/16)
thus x = -(1/4) +/- sqrt(13/16)
See?
John.
dkarolasz said:Solve by completing the square
4x^2+2x-3=0
(2x+1/2)2-1/2-3=0
(2x+1/2)2=7/2
Did I get this right?
I approach completing the square this way:
1) get the terms containing the variable on one side, and the constant term on the other side:
4x<SUP>2</SUP> + 2x = 3
2) Divide both sides by the coefficient of the square term:
x<SUP>2</SUP> + (1/2)x = 3/4
3) Multiply the coefficient of x by 1/2, square the result, and add the square to both sides of the equation. (1/2)*(1/2) is 1/4. (1/4)<SUP>2</SUP> is 1/16. Add 1/16 to both sides of the equation:
x<SUP>2</SUP> + (1/2)x + (1/16) = (3/4) + (1/16)
4) Write the left side as the square of a binomial, and do the arithmetic on the right side:
[ x + (1/4)]<SUP>2</SUP> = 13/16
5) Take the square root of both sides
x + (1/4) = +/- sqrt(13/16)
x + (1/4) = +/- sqrt(13)/4
6) Get x by itself....
x = (-1/4) +/- sqrt(13) / 4