first divide the equation with the coefficient of x^2 term. take the constant term to the other side.then add the square of the half of the coefficient of x term{(b/2)^2}.now convert the LHS side into (a+b)^2 or (a-b)^2 form.now solve the RHStake square root on both sides and solve the equation ....you will have 2 answershope you understood. :) :D

Say we have a simple expression like x2 + bx. Having x twice in the same expression can make life hard. What can we do?Well, with a little inspiration from Geometry we can convert it, like this:Completing the Square GeometryAs you can see x2 + bx can be rearranged nearly into a square ...... and we can complete the square with (b/2)2In Algebra it looks like this:x2 + bx + (b/2)2 = (x+b/2)2 "Complete the Square" So, by adding (b/2)2 we can complete the square.And (x+b/2)2 has x only once, which is easier to use.Keeping the BalanceNow ... we can't just add (b/2)2 without also subtracting it too! Otherwise the whole value changes.So let's see how to do it properly with an example:Start with: x^2 + 6x + 7 ("b" is 6 in this case) Complete the Square:x^2 + 6x + (6/2)^2 + 7 - (6/2)^2 Also subtract the new term Simplify it and we are done. simplifies to (x+3)^2 The result:x2 + 6x + 7 = (x+3)2 − 2And now x only appears once, and our job is done!A Shortcut ApproachLet us look at the result we want: (x+d)2 + eWhen we expand (x+d)2 we get x2 + 2dx + d2, so:x^2 + (6x) + [7] matches x^2 + (2dx) + [d^2+e]Now we can "force" an answer:We know that 6x must end up as 2dx, so d must be 3Next we see that 7 must become d2 + e = 9 + e, so e must be −2And we get the same result (x+3)2 − 2 as above! Now, let us look at a useful application: solving Quadratic Equations ...Solving General Quadratic Equations by Completing the SquareWe can complete the square to solve a Quadratic Equation (find where it is equal to zero).But a general Quadratic Equation can have a coefficient of a in front of x2:ax2 + bx + c = 0But that is easy to deal with ... just divide the whole equation by "a" first, then carry on:x2 + (b/a)x + c/a = 0StepsNow we can solve a Quadratic Equation in 5 steps:Step 1 Divide all terms by a (the coefficient of x2).Step 2 Move the number term (c/a) to the right side of the equation.Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.We now have something that looks like (x + p)2 = q, which can be solved rather easily:Step 4 Take the square root on both sides of the equation.Step 5 Subtract the number that remains on the left side of the equation to find x.