x^2+3x-183=0

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Solution for x^2+3x-183=0 equation:


Simplifying
x2 + 3x + -183 = 0

Reorder the terms:
-183 + 3x + x2 = 0

Solving
-183 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '183' to each side of the equation.
-183 + 3x + 183 + x2 = 0 + 183

Reorder the terms:
-183 + 183 + 3x + x2 = 0 + 183

Combine like terms: -183 + 183 = 0
0 + 3x + x2 = 0 + 183
3x + x2 = 0 + 183

Combine like terms: 0 + 183 = 183
3x + x2 = 183

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 = 183 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 183 + 2.25

Combine like terms: 183 + 2.25 = 185.25
2.25 + 3x + x2 = 185.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 185.25

Calculate the square root of the right side: 13.610657589

Break this problem into two subproblems by setting 
(x + 1.5) equal to 13.610657589 and -13.610657589.

Subproblem 1

x + 1.5 = 13.610657589 Simplifying x + 1.5 = 13.610657589 Reorder the terms: 1.5 + x = 13.610657589 Solving 1.5 + x = 13.610657589 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 = 13.610657589 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.610657589 + -1.5 x = 13.610657589 + -1.5 Combine like terms: 13.610657589 + -1.5 = 12.110657589 x = 12.110657589 Simplifying x = 12.110657589

Subproblem 2

x + 1.5 = -13.610657589 Simplifying x + 1.5 = -13.610657589 Reorder the terms: 1.5 + x = -13.610657589 Solving 1.5 + x = -13.610657589 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 = -13.610657589 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.610657589 + -1.5 x = -13.610657589 + -1.5 Combine like terms: -13.610657589 + -1.5 = -15.110657589 x = -15.110657589 Simplifying x = -15.110657589

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.110657589, -15.110657589}

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