x^2+3x=363

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Solution for x^2+3x=363 equation:


Simplifying
x2 + 3x = 363

Reorder the terms:
3x + x2 = 363

Solving
3x + x2 = 363

Solving for variable 'x'.

Reorder the terms:
-363 + 3x + x2 = 363 + -363

Combine like terms: 363 + -363 = 0
-363 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '363' to each side of the equation.
-363 + 3x + 363 + x2 = 0 + 363

Reorder the terms:
-363 + 363 + 3x + x2 = 0 + 363

Combine like terms: -363 + 363 = 0
0 + 3x + x2 = 0 + 363
3x + x2 = 0 + 363

Combine like terms: 0 + 363 = 363
3x + x2 = 363

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 = 363 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 363 + 2.25

Combine like terms: 363 + 2.25 = 365.25
2.25 + 3x + x2 = 365.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 365.25

Calculate the square root of the right side: 19.111514854

Break this problem into two subproblems by setting 
(x + 1.5) equal to 19.111514854 and -19.111514854.

Subproblem 1

x + 1.5 = 19.111514854 Simplifying x + 1.5 = 19.111514854 Reorder the terms: 1.5 + x = 19.111514854 Solving 1.5 + x = 19.111514854 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 = 19.111514854 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 19.111514854 + -1.5 x = 19.111514854 + -1.5 Combine like terms: 19.111514854 + -1.5 = 17.611514854 x = 17.611514854 Simplifying x = 17.611514854

Subproblem 2

x + 1.5 = -19.111514854 Simplifying x + 1.5 = -19.111514854 Reorder the terms: 1.5 + x = -19.111514854 Solving 1.5 + x = -19.111514854 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 = -19.111514854 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -19.111514854 + -1.5 x = -19.111514854 + -1.5 Combine like terms: -19.111514854 + -1.5 = -20.611514854 x = -20.611514854 Simplifying x = -20.611514854

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.611514854, -20.611514854}

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