x^2+3x+14=47.75

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Solution for x^2+3x+14=47.75 equation: 


Simplifying
x2 + 3x + 14 = 47.75

Reorder the terms:
14 + 3x + x2 = 47.75

Solving
14 + 3x + x2 = 47.75

Solving for variable 'x'.

Reorder the terms:
14 + -47.75 + 3x + x2 = 47.75 + -47.75

Combine like terms: 14 + -47.75 = -33.75
-33.75 + 3x + x2 = 47.75 + -47.75

Combine like terms: 47.75 + -47.75 = 0.00
-33.75 + 3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '33.75' to each side of the equation.
-33.75 + 3x + 33.75 + x2 = 0.00 + 33.75

Reorder the terms:
-33.75 + 33.75 + 3x + x2 = 0.00 + 33.75

Combine like terms: -33.75 + 33.75 = 0.00
0.00 + 3x + x2 = 0.00 + 33.75
3x + x2 = 0.00 + 33.75

Combine like terms: 0.00 + 33.75 = 33.75
3x + x2 = 33.75

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 = 33.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 33.75 + 2.25

Combine like terms: 33.75 + 2.25 = 36
2.25 + 3x + x2 = 36

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6 and -6.


Subproblem 1
x + 1.5 = 6

Simplifying
x + 1.5 = 6

Reorder the terms:
1.5 + x = 6

Solving
1.5 + x = 6

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 = 6 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6 + -1.5
x = 6 + -1.5

Combine like terms: 6 + -1.5 = 4.5
x = 4.5

Simplifying
x = 4.5


Subproblem 2
x + 1.5 = -6

Simplifying
x + 1.5 = -6

Reorder the terms:
1.5 + x = -6

Solving
1.5 + x = -6

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 = -6 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6 + -1.5
x = -6 + -1.5

Combine like terms: -6 + -1.5 = -7.5
x = -7.5

Simplifying
x = -7.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -7.5}

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