(x*x)+0.7x=13.4

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Solution for (x*x)+0.7x=13.4 equation: 


Simplifying
(x * x) + 0.7x = 13.4

Multiply x * x
(x2) + 0.7x = 13.4
x2 + 0.7x = 13.4

Reorder the terms:
0.7x + x2 = 13.4

Solving
0.7x + x2 = 13.4

Solving for variable 'x'.

Reorder the terms:
-13.4 + 0.7x + x2 = 13.4 + -13.4

Combine like terms: 13.4 + -13.4 = 0.0
-13.4 + 0.7x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '13.4' to each side of the equation.
-13.4 + 0.7x + 13.4 + x2 = 0.0 + 13.4

Reorder the terms:
-13.4 + 13.4 + 0.7x + x2 = 0.0 + 13.4

Combine like terms: -13.4 + 13.4 = 0.0
0.0 + 0.7x + x2 = 0.0 + 13.4
0.7x + x2 = 0.0 + 13.4

Combine like terms: 0.0 + 13.4 = 13.4
0.7x + x2 = 13.4

The x term is 0.7x.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7x + 0.1225 + x2 = 13.4 + 0.1225

Reorder the terms:
0.1225 + 0.7x + x2 = 13.4 + 0.1225

Combine like terms: 13.4 + 0.1225 = 13.5225
0.1225 + 0.7x + x2 = 13.5225

Factor a perfect square on the left side:
(x + 0.35)(x + 0.35) = 13.5225

Calculate the square root of the right side: 3.677295202

Break this problem into two subproblems by setting 
(x + 0.35) equal to 3.677295202 and -3.677295202.


Subproblem 1
x + 0.35 = 3.677295202

Simplifying
x + 0.35 = 3.677295202

Reorder the terms:
0.35 + x = 3.677295202

Solving
0.35 + x = 3.677295202

Solving for variable 'x'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + x = 3.677295202 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x = 3.677295202 + -0.35
x = 3.677295202 + -0.35

Combine like terms: 3.677295202 + -0.35 = 3.327295202
x = 3.327295202

Simplifying
x = 3.327295202


Subproblem 2
x + 0.35 = -3.677295202

Simplifying
x + 0.35 = -3.677295202

Reorder the terms:
0.35 + x = -3.677295202

Solving
0.35 + x = -3.677295202

Solving for variable 'x'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + x = -3.677295202 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x = -3.677295202 + -0.35
x = -3.677295202 + -0.35

Combine like terms: -3.677295202 + -0.35 = -4.027295202
x = -4.027295202

Simplifying
x = -4.027295202


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.327295202, -4.027295202}

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