x^2+3x-166=0

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Solution for x^2+3x-166=0 equation:


Simplifying
x2 + 3x + -166 = 0

Reorder the terms:
-166 + 3x + x2 = 0

Solving
-166 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '166' to each side of the equation.
-166 + 3x + 166 + x2 = 0 + 166

Reorder the terms:
-166 + 166 + 3x + x2 = 0 + 166

Combine like terms: -166 + 166 = 0
0 + 3x + x2 = 0 + 166
3x + x2 = 0 + 166

Combine like terms: 0 + 166 = 166
3x + x2 = 166

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 = 166 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 166 + 2.25

Combine like terms: 166 + 2.25 = 168.25
2.25 + 3x + x2 = 168.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 168.25

Calculate the square root of the right side: 12.971121771

Break this problem into two subproblems by setting 
(x + 1.5) equal to 12.971121771 and -12.971121771.

Subproblem 1

x + 1.5 = 12.971121771 Simplifying x + 1.5 = 12.971121771 Reorder the terms: 1.5 + x = 12.971121771 Solving 1.5 + x = 12.971121771 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 = 12.971121771 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.971121771 + -1.5 x = 12.971121771 + -1.5 Combine like terms: 12.971121771 + -1.5 = 11.471121771 x = 11.471121771 Simplifying x = 11.471121771

Subproblem 2

x + 1.5 = -12.971121771 Simplifying x + 1.5 = -12.971121771 Reorder the terms: 1.5 + x = -12.971121771 Solving 1.5 + x = -12.971121771 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 = -12.971121771 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.971121771 + -1.5 x = -12.971121771 + -1.5 Combine like terms: -12.971121771 + -1.5 = -14.471121771 x = -14.471121771 Simplifying x = -14.471121771

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.471121771, -14.471121771}

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