5x+3x^2=11

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Solution for 5x+3x^2=11 equation: 


Simplifying
5x + 3x2 = 11

Solving
5x + 3x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 5x + 3x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 5x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.666666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 1.666666667x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 1.666666667x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 3.666666667
1.666666667x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
1.666666667x + x2 = 3.666666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 3.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 3.666666667 + 0.6944444447

Combine like terms: 3.666666667 + 0.6944444447 = 4.3611111117
0.6944444447 + 1.666666667x + x2 = 4.3611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 4.3611111117

Calculate the square root of the right side: 2.088327348

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.088327348 and -2.088327348.


Subproblem 1
x + 0.8333333335 = 2.088327348

Simplifying
x + 0.8333333335 = 2.088327348

Reorder the terms:
0.8333333335 + x = 2.088327348

Solving
0.8333333335 + x = 2.088327348

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.088327348 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.088327348 + -0.8333333335
x = 2.088327348 + -0.8333333335

Combine like terms: 2.088327348 + -0.8333333335 = 1.2549940145
x = 1.2549940145

Simplifying
x = 1.2549940145


Subproblem 2
x + 0.8333333335 = -2.088327348

Simplifying
x + 0.8333333335 = -2.088327348

Reorder the terms:
0.8333333335 + x = -2.088327348

Solving
0.8333333335 + x = -2.088327348

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.088327348 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.088327348 + -0.8333333335
x = -2.088327348 + -0.8333333335

Combine like terms: -2.088327348 + -0.8333333335 = -2.9216606815
x = -2.9216606815

Simplifying
x = -2.9216606815


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2549940145, -2.9216606815}

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