(3x+0.05)+(x)(x+0.10)=7.50

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Solution for (3x+0.05)+(x)(x+0.10)=7.50 equation:


Simplifying
(3x + 0.05) + (x)(x + 0.10) = 7.50

Reorder the terms:
(0.05 + 3x) + (x)(x + 0.10) = 7.50

Remove parenthesis around (0.05 + 3x)
0.05 + 3x + (x)(x + 0.10) = 7.50

Reorder the terms:
0.05 + 3x + x(0.10 + x) = 7.50
0.05 + 3x + (0.10 * x + x * x) = 7.50
0.05 + 3x + (0.10x + x2) = 7.50

Combine like terms: 3x + 0.10x = 3.1x
0.05 + 3.1x + x2 = 7.50

Solving
0.05 + 3.1x + x2 = 7.50

Solving for variable 'x'.

Reorder the terms:
0.05 + -7.50 + 3.1x + x2 = 7.50 + -7.50

Combine like terms: 0.05 + -7.50 = -7.45
-7.45 + 3.1x + x2 = 7.50 + -7.50

Combine like terms: 7.50 + -7.50 = 0.00
-7.45 + 3.1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '7.45' to each side of the equation.
-7.45 + 3.1x + 7.45 + x2 = 0.00 + 7.45

Reorder the terms:
-7.45 + 7.45 + 3.1x + x2 = 0.00 + 7.45

Combine like terms: -7.45 + 7.45 = 0.00
0.00 + 3.1x + x2 = 0.00 + 7.45
3.1x + x2 = 0.00 + 7.45

Combine like terms: 0.00 + 7.45 = 7.45
3.1x + x2 = 7.45

The x term is 3.1x.  Take half its coefficient (1.55).
Square it (2.4025) and add it to both sides.

Add '2.4025' to each side of the equation.
3.1x + 2.4025 + x2 = 7.45 + 2.4025

Reorder the terms:
2.4025 + 3.1x + x2 = 7.45 + 2.4025

Combine like terms: 7.45 + 2.4025 = 9.8525
2.4025 + 3.1x + x2 = 9.8525

Factor a perfect square on the left side:
(x + 1.55)(x + 1.55) = 9.8525

Calculate the square root of the right side: 3.138869223

Break this problem into two subproblems by setting 
(x + 1.55) equal to 3.138869223 and -3.138869223.


Subproblem 1
x + 1.55 = 3.138869223

Simplifying
x + 1.55 = 3.138869223

Reorder the terms:
1.55 + x = 3.138869223

Solving
1.55 + x = 3.138869223

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = 3.138869223 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = 3.138869223 + -1.55
x = 3.138869223 + -1.55

Combine like terms: 3.138869223 + -1.55 = 1.588869223
x = 1.588869223

Simplifying
x = 1.588869223


Subproblem 2
x + 1.55 = -3.138869223

Simplifying
x + 1.55 = -3.138869223

Reorder the terms:
1.55 + x = -3.138869223

Solving
1.55 + x = -3.138869223

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = -3.138869223 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = -3.138869223 + -1.55
x = -3.138869223 + -1.55

Combine like terms: -3.138869223 + -1.55 = -4.688869223
x = -4.688869223

Simplifying
x = -4.688869223


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.588869223, -4.688869223}

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