[x^2+3x-15]=0

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


Simplifying
[x2 + 3x + -15] = 0

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

Remove brackets around [-15 + 3x + x2]
-15 + 3x + x2 = 0

Solving
-15 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 3x + 15 + x2 = 0 + 15

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

Combine like terms: -15 + 15 = 0
0 + 3x + x2 = 0 + 15
3x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
3x + x2 = 15

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 15 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 15 + 2.25

Combine like terms: 15 + 2.25 = 17.25
2.25 + 3x + x2 = 17.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + 1.5 = 4.153311931

Simplifying
x + 1.5 = 4.153311931

Reorder the terms:
1.5 + x = 4.153311931

Solving
1.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.153311931 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.153311931 + -1.5
x = 4.153311931 + -1.5

Combine like terms: 4.153311931 + -1.5 = 2.653311931
x = 2.653311931

Simplifying
x = 2.653311931


Subproblem 2
x + 1.5 = -4.153311931

Simplifying
x + 1.5 = -4.153311931

Reorder the terms:
1.5 + x = -4.153311931

Solving
1.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.153311931 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.153311931 + -1.5
x = -4.153311931 + -1.5

Combine like terms: -4.153311931 + -1.5 = -5.653311931
x = -5.653311931

Simplifying
x = -5.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.653311931, -5.653311931}

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