3x^2+10x-15=0

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Solution for 3x^2+10x-15=0 equation: 


Simplifying
3x2 + 10x + -15 = 0

Reorder the terms:
-15 + 10x + 3x2 = 0

Solving
-15 + 10x + 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 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 3.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3.333333333x + x2 = 0 + 5
3.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
3.333333333x + x2 = 5

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 5 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 5 + 2.777777779

Combine like terms: 5 + 2.777777779 = 7.777777779
2.777777779 + 3.333333333x + x2 = 7.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 7.777777779

Calculate the square root of the right side: 2.788866755

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.788866755 and -2.788866755.


Subproblem 1
x + 1.666666667 = 2.788866755

Simplifying
x + 1.666666667 = 2.788866755

Reorder the terms:
1.666666667 + x = 2.788866755

Solving
1.666666667 + x = 2.788866755

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 2.788866755 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 2.788866755 + -1.666666667
x = 2.788866755 + -1.666666667

Combine like terms: 2.788866755 + -1.666666667 = 1.122200088
x = 1.122200088

Simplifying
x = 1.122200088


Subproblem 2
x + 1.666666667 = -2.788866755

Simplifying
x + 1.666666667 = -2.788866755

Reorder the terms:
1.666666667 + x = -2.788866755

Solving
1.666666667 + x = -2.788866755

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -2.788866755 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -2.788866755 + -1.666666667
x = -2.788866755 + -1.666666667

Combine like terms: -2.788866755 + -1.666666667 = -4.455533422
x = -4.455533422

Simplifying
x = -4.455533422


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.122200088, -4.455533422}

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