-3x^2+22x+15=0

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Solution for -3x^2+22x+15=0 equation: 


Simplifying
-3x2 + 22x + 15 = 0

Reorder the terms:
15 + 22x + -3x2 = 0

Solving
15 + 22x + -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'.
-5 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -7.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -7.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7.333333333x + x2 = 0 + 5
-7.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-7.333333333x + x2 = 5

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 5 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 5 + 13.44444445

Combine like terms: 5 + 13.44444445 = 18.44444445
13.44444445 + -7.333333333x + x2 = 18.44444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 18.44444445

Calculate the square root of the right side: 4.294699576

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 4.294699576 and -4.294699576.


Subproblem 1
x + -3.666666667 = 4.294699576

Simplifying
x + -3.666666667 = 4.294699576

Reorder the terms:
-3.666666667 + x = 4.294699576

Solving
-3.666666667 + x = 4.294699576

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 4.294699576 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 4.294699576 + 3.666666667
x = 4.294699576 + 3.666666667

Combine like terms: 4.294699576 + 3.666666667 = 7.961366243
x = 7.961366243

Simplifying
x = 7.961366243


Subproblem 2
x + -3.666666667 = -4.294699576

Simplifying
x + -3.666666667 = -4.294699576

Reorder the terms:
-3.666666667 + x = -4.294699576

Solving
-3.666666667 + x = -4.294699576

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -4.294699576 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -4.294699576 + 3.666666667
x = -4.294699576 + 3.666666667

Combine like terms: -4.294699576 + 3.666666667 = -0.628032909
x = -0.628032909

Simplifying
x = -0.628032909


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.961366243, -0.628032909}

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