x^2+3x-2.25=42.25

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Solution for x^2+3x-2.25=42.25 equation: 


Simplifying
x2 + 3x + -2.25 = 42.25

Reorder the terms:
-2.25 + 3x + x2 = 42.25

Solving
-2.25 + 3x + x2 = 42.25

Solving for variable 'x'.

Reorder the terms:
-2.25 + -42.25 + 3x + x2 = 42.25 + -42.25

Combine like terms: -2.25 + -42.25 = -44.5
-44.5 + 3x + x2 = 42.25 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
-44.5 + 3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '44.5' to each side of the equation.
-44.5 + 3x + 44.5 + x2 = 0.00 + 44.5

Reorder the terms:
-44.5 + 44.5 + 3x + x2 = 0.00 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + 3x + x2 = 0.00 + 44.5
3x + x2 = 0.00 + 44.5

Combine like terms: 0.00 + 44.5 = 44.5
3x + x2 = 44.5

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 = 44.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 44.5 + 2.25

Combine like terms: 44.5 + 2.25 = 46.75
2.25 + 3x + x2 = 46.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 46.75

Calculate the square root of the right side: 6.837397166

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.837397166 and -6.837397166.


Subproblem 1
x + 1.5 = 6.837397166

Simplifying
x + 1.5 = 6.837397166

Reorder the terms:
1.5 + x = 6.837397166

Solving
1.5 + x = 6.837397166

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 = 6.837397166 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6.837397166 + -1.5
x = 6.837397166 + -1.5

Combine like terms: 6.837397166 + -1.5 = 5.337397166
x = 5.337397166

Simplifying
x = 5.337397166


Subproblem 2
x + 1.5 = -6.837397166

Simplifying
x + 1.5 = -6.837397166

Reorder the terms:
1.5 + x = -6.837397166

Solving
1.5 + x = -6.837397166

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 = -6.837397166 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6.837397166 + -1.5
x = -6.837397166 + -1.5

Combine like terms: -6.837397166 + -1.5 = -8.337397166
x = -8.337397166

Simplifying
x = -8.337397166


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.337397166, -8.337397166}

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