quadratic equation by completing the square?

Question

Please answer!! algebra.. quadratic formula by factoring.?
If the length of each side of a square is increased by 5cm, the area is multiplied by 4. What is the length of the original side of the square..
[please show the step by step solving]

Answer 1

Let x = length of sides of original square.

We know that the formula of a square is x² ; therefore

A = x²

Increasing the length of a side of a square is interpreted as
x + 5, and doing so means the area is 4 times bigger. That is

4A = (x + 5)²

Two equations, two unknowns.

A = x²
4A = (x + 5)²

Substitute A = x² into the second equation, and solve for x.

4x² = (x + 5)²

Let's move everything to the left hand side and factor as a difference of squares; it saves a step.

4x² - (x + 5)² = 0

[2x - (x + 5)] [2x + (x + 5)] = 0

[2x - x - 5] [2x + x + 5] = 0

[x - 5] [3x + 5] = 0

This means

x - 5 = 0, or
3x + 5 = 0

x = 5

x = -5/3

But x = -5/3 is extraneous (we cannot have a negative length), so we reject it.

x = 5.

Answer 2

Let the length of the original side of the square be x.

(x+5)^2 = 4(x^2 )
By expansion,
x^2 + 10x + 25 = 4(x^2)
3x^2 - 10x - 25 = 0
(3x + 5)(x - 5) = 0
Therefore, x = -5/3 or 5
Since x cannot be negative, x = 5

Answer 3

See the link, especially "Completing the Square: diagram." The process actually has a physical significance which is why it refers to squares.