(X+0.34)(X+0.23)=2

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Solution for (X+0.34)(X+0.23)=2 equation:


Simplifying
(X + 0.34)(X + 0.23) = 2

Reorder the terms:
(0.34 + X)(X + 0.23) = 2

Reorder the terms:
(0.34 + X)(0.23 + X) = 2

Multiply (0.34 + X) * (0.23 + X)
(0.34(0.23 + X) + X(0.23 + X)) = 2
((0.23 * 0.34 + X * 0.34) + X(0.23 + X)) = 2
((0.0782 + 0.34X) + X(0.23 + X)) = 2
(0.0782 + 0.34X + (0.23 * X + X * X)) = 2
(0.0782 + 0.34X + (0.23X + X2)) = 2

Combine like terms: 0.34X + 0.23X = 0.57X
(0.0782 + 0.57X + X2) = 2

Solving
0.0782 + 0.57X + X2 = 2

Solving for variable 'X'.

Reorder the terms:
0.0782 + -2 + 0.57X + X2 = 2 + -2

Combine like terms: 0.0782 + -2 = -1.9218
-1.9218 + 0.57X + X2 = 2 + -2

Combine like terms: 2 + -2 = 0
-1.9218 + 0.57X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1.9218' to each side of the equation.
-1.9218 + 0.57X + 1.9218 + X2 = 0 + 1.9218

Reorder the terms:
-1.9218 + 1.9218 + 0.57X + X2 = 0 + 1.9218

Combine like terms: -1.9218 + 1.9218 = 0.0000
0.0000 + 0.57X + X2 = 0 + 1.9218
0.57X + X2 = 0 + 1.9218

Combine like terms: 0 + 1.9218 = 1.9218
0.57X + X2 = 1.9218

The X term is 0.57X.  Take half its coefficient (0.285).
Square it (0.081225) and add it to both sides.

Add '0.081225' to each side of the equation.
0.57X + 0.081225 + X2 = 1.9218 + 0.081225

Reorder the terms:
0.081225 + 0.57X + X2 = 1.9218 + 0.081225

Combine like terms: 1.9218 + 0.081225 = 2.003025
0.081225 + 0.57X + X2 = 2.003025

Factor a perfect square on the left side:
(X + 0.285)(X + 0.285) = 2.003025

Calculate the square root of the right side: 1.415282657

Break this problem into two subproblems by setting 
(X + 0.285) equal to 1.415282657 and -1.415282657.

Subproblem 1

X + 0.285 = 1.415282657 Simplifying X + 0.285 = 1.415282657 Reorder the terms: 0.285 + X = 1.415282657 Solving 0.285 + X = 1.415282657 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.285' to each side of the equation. 0.285 + -0.285 + X = 1.415282657 + -0.285 Combine like terms: 0.285 + -0.285 = 0.000 0.000 + X = 1.415282657 + -0.285 X = 1.415282657 + -0.285 Combine like terms: 1.415282657 + -0.285 = 1.130282657 X = 1.130282657 Simplifying X = 1.130282657

Subproblem 2

X + 0.285 = -1.415282657 Simplifying X + 0.285 = -1.415282657 Reorder the terms: 0.285 + X = -1.415282657 Solving 0.285 + X = -1.415282657 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.285' to each side of the equation. 0.285 + -0.285 + X = -1.415282657 + -0.285 Combine like terms: 0.285 + -0.285 = 0.000 0.000 + X = -1.415282657 + -0.285 X = -1.415282657 + -0.285 Combine like terms: -1.415282657 + -0.285 = -1.700282657 X = -1.700282657 Simplifying X = -1.700282657

Solution

The solution to the problem is based on the solutions from the subproblems. X = {1.130282657, -1.700282657}

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