X^2+3X+2=224

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Solution for X^2+3X+2=224 equation:


Simplifying
X2 + 3X + 2 = 224

Reorder the terms:
2 + 3X + X2 = 224

Solving
2 + 3X + X2 = 224

Solving for variable 'X'.

Reorder the terms:
2 + -224 + 3X + X2 = 224 + -224

Combine like terms: 2 + -224 = -222
-222 + 3X + X2 = 224 + -224

Combine like terms: 224 + -224 = 0
-222 + 3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '222' to each side of the equation.
-222 + 3X + 222 + X2 = 0 + 222

Reorder the terms:
-222 + 222 + 3X + X2 = 0 + 222

Combine like terms: -222 + 222 = 0
0 + 3X + X2 = 0 + 222
3X + X2 = 0 + 222

Combine like terms: 0 + 222 = 222
3X + X2 = 222

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 = 222 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 222 + 2.25

Combine like terms: 222 + 2.25 = 224.25
2.25 + 3X + X2 = 224.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 224.25

Calculate the square root of the right side: 14.974979132

Break this problem into two subproblems by setting 
(X + 1.5) equal to 14.974979132 and -14.974979132.

Subproblem 1

X + 1.5 = 14.974979132 Simplifying X + 1.5 = 14.974979132 Reorder the terms: 1.5 + X = 14.974979132 Solving 1.5 + X = 14.974979132 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 = 14.974979132 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 14.974979132 + -1.5 X = 14.974979132 + -1.5 Combine like terms: 14.974979132 + -1.5 = 13.474979132 X = 13.474979132 Simplifying X = 13.474979132

Subproblem 2

X + 1.5 = -14.974979132 Simplifying X + 1.5 = -14.974979132 Reorder the terms: 1.5 + X = -14.974979132 Solving 1.5 + X = -14.974979132 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 = -14.974979132 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -14.974979132 + -1.5 X = -14.974979132 + -1.5 Combine like terms: -14.974979132 + -1.5 = -16.474979132 X = -16.474979132 Simplifying X = -16.474979132

Solution

The solution to the problem is based on the solutions from the subproblems. X = {13.474979132, -16.474979132}

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