(2x+3)(2x+3.25)=0

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Solution for (2x+3)(2x+3.25)=0 equation: 


Simplifying
(2x + 3)(2x + 3.25) = 0

Reorder the terms:
(3 + 2x)(2x + 3.25) = 0

Reorder the terms:
(3 + 2x)(3.25 + 2x) = 0

Multiply (3 + 2x) * (3.25 + 2x)
(3(3.25 + 2x) + 2x * (3.25 + 2x)) = 0
((3.25 * 3 + 2x * 3) + 2x * (3.25 + 2x)) = 0
((9.75 + 6x) + 2x * (3.25 + 2x)) = 0
(9.75 + 6x + (3.25 * 2x + 2x * 2x)) = 0
(9.75 + 6x + (6.5x + 4x2)) = 0

Combine like terms: 6x + 6.5x = 12.5x
(9.75 + 12.5x + 4x2) = 0

Solving
9.75 + 12.5x + 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'.
2.4375 + 3.125x + x2 = 0

Move the constant term to the right:

Add '-2.4375' to each side of the equation.
2.4375 + 3.125x + -2.4375 + x2 = 0 + -2.4375

Reorder the terms:
2.4375 + -2.4375 + 3.125x + x2 = 0 + -2.4375

Combine like terms: 2.4375 + -2.4375 = 0.0000
0.0000 + 3.125x + x2 = 0 + -2.4375
3.125x + x2 = 0 + -2.4375

Combine like terms: 0 + -2.4375 = -2.4375
3.125x + x2 = -2.4375

The x term is 3.125x.  Take half its coefficient (1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
3.125x + 2.44140625 + x2 = -2.4375 + 2.44140625

Reorder the terms:
2.44140625 + 3.125x + x2 = -2.4375 + 2.44140625

Combine like terms: -2.4375 + 2.44140625 = 0.00390625
2.44140625 + 3.125x + x2 = 0.00390625

Factor a perfect square on the left side:
(x + 1.5625)(x + 1.5625) = 0.00390625

Calculate the square root of the right side: 0.0625

Break this problem into two subproblems by setting 
(x + 1.5625) equal to 0.0625 and -0.0625.


Subproblem 1
x + 1.5625 = 0.0625

Simplifying
x + 1.5625 = 0.0625

Reorder the terms:
1.5625 + x = 0.0625

Solving
1.5625 + x = 0.0625

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + x = 0.0625 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + x = 0.0625 + -1.5625
x = 0.0625 + -1.5625

Combine like terms: 0.0625 + -1.5625 = -1.5
x = -1.5

Simplifying
x = -1.5


Subproblem 2
x + 1.5625 = -0.0625

Simplifying
x + 1.5625 = -0.0625

Reorder the terms:
1.5625 + x = -0.0625

Solving
1.5625 + x = -0.0625

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + x = -0.0625 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + x = -0.0625 + -1.5625
x = -0.0625 + -1.5625

Combine like terms: -0.0625 + -1.5625 = -1.625
x = -1.625

Simplifying
x = -1.625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.5, -1.625}

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