Question

solve the equation by the method of completing square (x+2) (x+1) =(4x-1) (x-2)​

Answer 1

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Solve the quadratic equation x^2 + 4x +1 = 0 by completing the square. The first step is to divide the coefficient of x by 2, and add this to x (this is our value of 'a' to go inside our bracket). We then square this value of a and subtract it outside the bracket. We have our equation in completed square form.

Answer 2

Answer:

The first step is to divide the coefficient of x by 2, and add this to x (this is our value of 'a' to go inside our bracket). We then square this value of a and subtract it outside the bracket.

In our example it will look like this:

(x+2)2 - 4 + 1 = 0

(x+2)2 - 3 = 0

We have our equation in completed square form.

[There is a quick way to check we've got this right by expanding out this equation quickly:

(x+2)(x+2) - 3 = 0

x2 + 4x + 4 - 3 = 0

x2 + 4x +1 = 0

We're back to our original equation, so we know we've got it right. Let's go and solve our equation in completed square form.]

We simply rearrange for x:

(x+2)2 - 3 = 0

Add 3 to both sides.

(x+2)2 = 3

Take the square root of both sides. This splits into two possible cases:

Case 1: Positive square root of 3

x+2 = + sqrt(3)

x = - 2 + sqrt(3)

Case 2: Negative square root of 3

x+2 = - sqrt(3)

x = - 2 - sqrt(3)

So our final answer is...

x = - 2 + sqrt(3)

x = - 2 - sqrt(3)