(x+0.7)(x+0.7)=2.91

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Solution for (x+0.7)(x+0.7)=2.91 equation: 


Simplifying
(x + 0.7)(x + 0.7) = 2.91

Reorder the terms:
(0.7 + x)(x + 0.7) = 2.91

Reorder the terms:
(0.7 + x)(0.7 + x) = 2.91

Multiply (0.7 + x) * (0.7 + x)
(0.7(0.7 + x) + x(0.7 + x)) = 2.91
((0.7 * 0.7 + x * 0.7) + x(0.7 + x)) = 2.91
((0.49 + 0.7x) + x(0.7 + x)) = 2.91
(0.49 + 0.7x + (0.7 * x + x * x)) = 2.91
(0.49 + 0.7x + (0.7x + x2)) = 2.91

Combine like terms: 0.7x + 0.7x = 1.4x
(0.49 + 1.4x + x2) = 2.91

Solving
0.49 + 1.4x + x2 = 2.91

Solving for variable 'x'.

Reorder the terms:
0.49 + -2.91 + 1.4x + x2 = 2.91 + -2.91

Combine like terms: 0.49 + -2.91 = -2.42
-2.42 + 1.4x + x2 = 2.91 + -2.91

Combine like terms: 2.91 + -2.91 = 0.00
-2.42 + 1.4x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2.42' to each side of the equation.
-2.42 + 1.4x + 2.42 + x2 = 0.00 + 2.42

Reorder the terms:
-2.42 + 2.42 + 1.4x + x2 = 0.00 + 2.42

Combine like terms: -2.42 + 2.42 = 0.00
0.00 + 1.4x + x2 = 0.00 + 2.42
1.4x + x2 = 0.00 + 2.42

Combine like terms: 0.00 + 2.42 = 2.42
1.4x + x2 = 2.42

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 2.42 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 2.42 + 0.49

Combine like terms: 2.42 + 0.49 = 2.91
0.49 + 1.4x + x2 = 2.91

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 2.91

Calculate the square root of the right side: 1.705872211

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.705872211 and -1.705872211.


Subproblem 1
x + 0.7 = 1.705872211

Simplifying
x + 0.7 = 1.705872211

Reorder the terms:
0.7 + x = 1.705872211

Solving
0.7 + x = 1.705872211

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = 1.705872211 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 1.705872211 + -0.7
x = 1.705872211 + -0.7

Combine like terms: 1.705872211 + -0.7 = 1.005872211
x = 1.005872211

Simplifying
x = 1.005872211


Subproblem 2
x + 0.7 = -1.705872211

Simplifying
x + 0.7 = -1.705872211

Reorder the terms:
0.7 + x = -1.705872211

Solving
0.7 + x = -1.705872211

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = -1.705872211 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -1.705872211 + -0.7
x = -1.705872211 + -0.7

Combine like terms: -1.705872211 + -0.7 = -2.405872211
x = -2.405872211

Simplifying
x = -2.405872211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.005872211, -2.405872211}

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