Question

how to solve quadratic equation by square method easily​

Answer 1

Bonjour!

Your Question Is:

how to solve quadratic equation by square method easily

Hope This Will Help You✔️✔️

Answer:

For those of you in a hurry, I can tell you that: d = b2a

and: e = c − b24a

But if you have time, let me show you how to "Complete the Square" yourself.

Completing the Square

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 Geometry

As you can see x2 + bx can be rearranged nearly into a square ...

... and we can complete the square with (b/2)2

In 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 Balance

Now ... 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 − 2

And now x only appears once, and our job is done!

A Shortcut Approach

Here is a quick way to get an answer. You may like this method.

First think about the result we want: (x+d)2 + e

After expanding (x+d)2 we get: x2 + 2dx + d2 + e

Now see if we can turn our example into that form to discover d and e

Example: try to fit x2 + 6x + 7 into x2 + 2dx + d2 + e

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 3

Next we see that 7 must become d2 + e = 9 + e, so e must be −2

And we get the same result (x+3)2 − 2 as above!

Answer 2

Completing the Square is a method used to solve a quadratic equation by changing the form of the

equation so that the left side is a perfect square trinomial . To solve a x 2 + b x + c = 0 by completing the

square : 1. Transform the equation so that the constant term, , is alone on the right side.