-3x^2+5x+15=0

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Solution for -3x^2+5x+15=0 equation: 


Simplifying
-3x2 + 5x + 15 = 0

Reorder the terms:
15 + 5x + -3x2 = 0

Solving
15 + 5x + -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 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1.666666667x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -1.666666667x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1.666666667x + x2 = 0 + 5
-1.666666667x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1.666666667x + x2 = 5

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 = 5 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 5 + 0.6944444447

Combine like terms: 5 + 0.6944444447 = 5.6944444447
0.6944444447 + -1.666666667x + x2 = 5.6944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 5.6944444447

Calculate the square root of the right side: 2.386303511

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 2.386303511 and -2.386303511.


Subproblem 1
x + -0.8333333335 = 2.386303511

Simplifying
x + -0.8333333335 = 2.386303511

Reorder the terms:
-0.8333333335 + x = 2.386303511

Solving
-0.8333333335 + x = 2.386303511

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 = 2.386303511 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 2.386303511 + 0.8333333335
x = 2.386303511 + 0.8333333335

Combine like terms: 2.386303511 + 0.8333333335 = 3.2196368445
x = 3.2196368445

Simplifying
x = 3.2196368445


Subproblem 2
x + -0.8333333335 = -2.386303511

Simplifying
x + -0.8333333335 = -2.386303511

Reorder the terms:
-0.8333333335 + x = -2.386303511

Solving
-0.8333333335 + x = -2.386303511

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 = -2.386303511 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -2.386303511 + 0.8333333335
x = -2.386303511 + 0.8333333335

Combine like terms: -2.386303511 + 0.8333333335 = -1.5529701775
x = -1.5529701775

Simplifying
x = -1.5529701775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2196368445, -1.5529701775}

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