x2-x-1806=0 by completing the square
x^2-x-1806=0
x^2-x=1806
x^2-x+(1/2)^2=1806+(1/2)^2
(x-1/2)^2=1806+1/4
(x-1/2)^2=7224+1/4
(x-1/2)^2=7225/4
as going
x^2-x+1/4=1806+1/4
(x-1/2)^2=( ? ) squared.
x-1/2= +- sqrt (1806+1/4)
Agyee ka solution nai hay na upper walay question may
Ah, completing the square, a classic math trick! Let's attempt it, shall we?
To complete the square for the quadratic equation x^2 - x - 1806 = 0, we need to focus on the coefficient of the x term, which is -1.
Step 1: Move the constant term to the right side of the equation:
x^2 - x = 1806
Step 2: Take half of the coefficient of the x term (-1/2) and square it to get (1/4):
x^2 - x + (1/4) = 1806 + (1/4)
Step 3: Simplify the right side of the equation:
x^2 - x + (1/4) = 1806.25
Step 4: Now, we can rewrite the left side as a perfect square trinomial:
(x - 1/2)^2 = 1806.25
Ta-da! We have completed the square. I hope you enjoyed this little math journey.
To solve the quadratic equation x^2 - x - 1806 = 0 by completing the square, follow these steps:
Step 1: Move the constant term (1806) to the other side of the equation:
x^2 - x = 1806
Step 2: Take half of the coefficient of the x-term (-1/2) and square it:
(-1/2)^2 = 1/4
Step 3: Add the computed value from step 2 to both sides of the equation:
x^2 - x + 1/4 = 1806 + 1/4
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 1/2)^2 = 1806 + 1/4
Step 5: Simplify the right side of the equation:
(x - 1/2)^2 = 7225/4
Step 6: Take the square root of both sides of the equation:
x - 1/2 = ± √(7225/4)
Step 7: Solve for x by adding 1/2 to both sides of the equation:
x = 1/2 ± √(7225/4)
Step 8: Simplify the right side of the equation:
x = 1/2 ± √7225/2
So the solutions to the quadratic equation x^2 - x - 1806 = 0, obtained by completing the square, are given by:
x = 1/2 + √(7225/2)
x = 1/2 - √(7225/2)