x^2+1.9x=20

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Solution for x^2+1.9x=20 equation: 


Simplifying
x2 + 1.9x = 20

Reorder the terms:
1.9x + x2 = 20

Solving
1.9x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 1.9x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 1.9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 1.9x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 1.9x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 1.9x + x2 = 0 + 20
1.9x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
1.9x + x2 = 20

The x term is 1.9x.  Take half its coefficient (0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
1.9x + 0.9025 + x2 = 20 + 0.9025

Reorder the terms:
0.9025 + 1.9x + x2 = 20 + 0.9025

Combine like terms: 20 + 0.9025 = 20.9025
0.9025 + 1.9x + x2 = 20.9025

Factor a perfect square on the left side:
(x + 0.95)(x + 0.95) = 20.9025

Calculate the square root of the right side: 4.571925196

Break this problem into two subproblems by setting 
(x + 0.95) equal to 4.571925196 and -4.571925196.


Subproblem 1
x + 0.95 = 4.571925196

Simplifying
x + 0.95 = 4.571925196

Reorder the terms:
0.95 + x = 4.571925196

Solving
0.95 + x = 4.571925196

Solving for variable 'x'.

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

Add '-0.95' to each side of the equation.
0.95 + -0.95 + x = 4.571925196 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + x = 4.571925196 + -0.95
x = 4.571925196 + -0.95

Combine like terms: 4.571925196 + -0.95 = 3.621925196
x = 3.621925196

Simplifying
x = 3.621925196


Subproblem 2
x + 0.95 = -4.571925196

Simplifying
x + 0.95 = -4.571925196

Reorder the terms:
0.95 + x = -4.571925196

Solving
0.95 + x = -4.571925196

Solving for variable 'x'.

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

Add '-0.95' to each side of the equation.
0.95 + -0.95 + x = -4.571925196 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + x = -4.571925196 + -0.95
x = -4.571925196 + -0.95

Combine like terms: -4.571925196 + -0.95 = -5.521925196
x = -5.521925196

Simplifying
x = -5.521925196


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.621925196, -5.521925196}

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