2x^2+x^2+14x-45=0

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Solution for 2x^2+x^2+14x-45=0 equation: 


Simplifying
2x2 + x2 + 14x + -45 = 0

Reorder the terms:
-45 + 14x + 2x2 + x2 = 0

Combine like terms: 2x2 + x2 = 3x2
-45 + 14x + 3x2 = 0

Solving
-45 + 14x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-15 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 4.666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 4.666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 4.666666667x + x2 = 0 + 15
4.666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
4.666666667x + x2 = 15

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 15 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 15 + 5.444444448

Combine like terms: 15 + 5.444444448 = 20.444444448
5.444444448 + 4.666666667x + x2 = 20.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 20.444444448

Calculate the square root of the right side: 4.521553322

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 4.521553322 and -4.521553322.


Subproblem 1
x + 2.333333334 = 4.521553322

Simplifying
x + 2.333333334 = 4.521553322

Reorder the terms:
2.333333334 + x = 4.521553322

Solving
2.333333334 + x = 4.521553322

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 4.521553322 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 4.521553322 + -2.333333334
x = 4.521553322 + -2.333333334

Combine like terms: 4.521553322 + -2.333333334 = 2.188219988
x = 2.188219988

Simplifying
x = 2.188219988


Subproblem 2
x + 2.333333334 = -4.521553322

Simplifying
x + 2.333333334 = -4.521553322

Reorder the terms:
2.333333334 + x = -4.521553322

Solving
2.333333334 + x = -4.521553322

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -4.521553322 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -4.521553322 + -2.333333334
x = -4.521553322 + -2.333333334

Combine like terms: -4.521553322 + -2.333333334 = -6.854886656
x = -6.854886656

Simplifying
x = -6.854886656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.188219988, -6.854886656}

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