(2x+0.75)(2x+0.75)=

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Solution for (2x+0.75)(2x+0.75)= equation:


Simplifying
(2x + 0.75)(2x + 0.75) = 0

Reorder the terms:
(0.75 + 2x)(2x + 0.75) = 0

Reorder the terms:
(0.75 + 2x)(0.75 + 2x) = 0

Multiply (0.75 + 2x) * (0.75 + 2x)
(0.75(0.75 + 2x) + 2x * (0.75 + 2x)) = 0
((0.75 * 0.75 + 2x * 0.75) + 2x * (0.75 + 2x)) = 0
((0.5625 + 1.5x) + 2x * (0.75 + 2x)) = 0
(0.5625 + 1.5x + (0.75 * 2x + 2x * 2x)) = 0
(0.5625 + 1.5x + (1.5x + 4x2)) = 0

Combine like terms: 1.5x + 1.5x = 3x
(0.5625 + 3x + 4x2) = 0

Solving
0.5625 + 3x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.140625 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.140625' to each side of the equation.
0.140625 + 0.75x + -0.140625 + x2 = 0 + -0.140625

Reorder the terms:
0.140625 + -0.140625 + 0.75x + x2 = 0 + -0.140625

Combine like terms: 0.140625 + -0.140625 = 0.000000
0.000000 + 0.75x + x2 = 0 + -0.140625
0.75x + x2 = 0 + -0.140625

Combine like terms: 0 + -0.140625 = -0.140625
0.75x + x2 = -0.140625

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.140625 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.140625 + 0.140625

Combine like terms: -0.140625 + 0.140625 = 0.000000
0.140625 + 0.75x + x2 = 0.000000

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.000000

Calculate the square root of the right side: 0.000000

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.000000 and 0.000000.

Subproblem 1

x + 0.375 = 0.000000 Simplifying x + 0.375 = 0.000000 Reorder the terms: 0.375 + x = 0.000000 Solving 0.375 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.000000 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.000000 + -0.375 x = 0.000000 + -0.375 Combine like terms: 0.000000 + -0.375 = -0.375 x = -0.375 Simplifying x = -0.375

Subproblem 2

x + 0.375 = 0.000000 Simplifying x + 0.375 = 0.000000 Reorder the terms: 0.375 + x = 0.000000 Solving 0.375 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.000000 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.000000 + -0.375 x = 0.000000 + -0.375 Combine like terms: 0.000000 + -0.375 = -0.375 x = -0.375 Simplifying x = -0.375

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.375, -0.375}

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