x(x+0.13)=0.051

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Solution for x(x+0.13)=0.051 equation: 


Simplifying
x(x + 0.13) = 0.051

Reorder the terms:
x(0.13 + x) = 0.051
(0.13 * x + x * x) = 0.051
(0.13x + x2) = 0.051

Solving
0.13x + x2 = 0.051

Solving for variable 'x'.

Reorder the terms:
-0.051 + 0.13x + x2 = 0.051 + -0.051

Combine like terms: 0.051 + -0.051 = 0.000
-0.051 + 0.13x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.051' to each side of the equation.
-0.051 + 0.13x + 0.051 + x2 = 0.000 + 0.051

Reorder the terms:
-0.051 + 0.051 + 0.13x + x2 = 0.000 + 0.051

Combine like terms: -0.051 + 0.051 = 0.000
0.000 + 0.13x + x2 = 0.000 + 0.051
0.13x + x2 = 0.000 + 0.051

Combine like terms: 0.000 + 0.051 = 0.051
0.13x + x2 = 0.051

The x term is 0.13x.  Take half its coefficient (0.065).
Square it (0.004225) and add it to both sides.

Add '0.004225' to each side of the equation.
0.13x + 0.004225 + x2 = 0.051 + 0.004225

Reorder the terms:
0.004225 + 0.13x + x2 = 0.051 + 0.004225

Combine like terms: 0.051 + 0.004225 = 0.055225
0.004225 + 0.13x + x2 = 0.055225

Factor a perfect square on the left side:
(x + 0.065)(x + 0.065) = 0.055225

Calculate the square root of the right side: 0.235

Break this problem into two subproblems by setting 
(x + 0.065) equal to 0.235 and -0.235.


Subproblem 1
x + 0.065 = 0.235

Simplifying
x + 0.065 = 0.235

Reorder the terms:
0.065 + x = 0.235

Solving
0.065 + x = 0.235

Solving for variable 'x'.

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

Add '-0.065' to each side of the equation.
0.065 + -0.065 + x = 0.235 + -0.065

Combine like terms: 0.065 + -0.065 = 0.000
0.000 + x = 0.235 + -0.065
x = 0.235 + -0.065

Combine like terms: 0.235 + -0.065 = 0.17
x = 0.17

Simplifying
x = 0.17


Subproblem 2
x + 0.065 = -0.235

Simplifying
x + 0.065 = -0.235

Reorder the terms:
0.065 + x = -0.235

Solving
0.065 + x = -0.235

Solving for variable 'x'.

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

Add '-0.065' to each side of the equation.
0.065 + -0.065 + x = -0.235 + -0.065

Combine like terms: 0.065 + -0.065 = 0.000
0.000 + x = -0.235 + -0.065
x = -0.235 + -0.065

Combine like terms: -0.235 + -0.065 = -0.3
x = -0.3

Simplifying
x = -0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.17, -0.3}

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