(x+2)(x+2)=0.25

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Solution for (x+2)(x+2)=0.25 equation:


Simplifying
(x + 2)(x + 2) = 0.25

Reorder the terms:
(2 + x)(x + 2) = 0.25

Reorder the terms:
(2 + x)(2 + x) = 0.25

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) = 0.25
((2 * 2 + x * 2) + x(2 + x)) = 0.25
((4 + 2x) + x(2 + x)) = 0.25
(4 + 2x + (2 * x + x * x)) = 0.25
(4 + 2x + (2x + x2)) = 0.25

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) = 0.25

Solving
4 + 4x + x2 = 0.25

Solving for variable 'x'.

Reorder the terms:
4 + -0.25 + 4x + x2 = 0.25 + -0.25

Combine like terms: 4 + -0.25 = 3.75
3.75 + 4x + x2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
3.75 + 4x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 4x + -3.75 + x2 = 0.00 + -3.75

Reorder the terms:
3.75 + -3.75 + 4x + x2 = 0.00 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 4x + x2 = 0.00 + -3.75
4x + x2 = 0.00 + -3.75

Combine like terms: 0.00 + -3.75 = -3.75
4x + x2 = -3.75

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -3.75 + 4

Reorder the terms:
4 + 4x + x2 = -3.75 + 4

Combine like terms: -3.75 + 4 = 0.25
4 + 4x + x2 = 0.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + 2) equal to 0.5 and -0.5.

Subproblem 1

x + 2 = 0.5 Simplifying x + 2 = 0.5 Reorder the terms: 2 + x = 0.5 Solving 2 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.5 + -2 x = 0.5 + -2 Combine like terms: 0.5 + -2 = -1.5 x = -1.5 Simplifying x = -1.5

Subproblem 2

x + 2 = -0.5 Simplifying x + 2 = -0.5 Reorder the terms: 2 + x = -0.5 Solving 2 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.5 + -2 x = -0.5 + -2 Combine like terms: -0.5 + -2 = -2.5 x = -2.5 Simplifying x = -2.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.5, -2.5}

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