-37x^2+18x+163=0

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Solution for -37x^2+18x+163=0 equation:


Simplifying
-37x2 + 18x + 163 = 0

Reorder the terms:
163 + 18x + -37x2 = 0

Solving
163 + 18x + -37x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-37 the coefficient of the squared term: 

Divide each side by '-37'.
-4.405405405 + -0.4864864865x + x2 = 0

Move the constant term to the right:

Add '4.405405405' to each side of the equation.
-4.405405405 + -0.4864864865x + 4.405405405 + x2 = 0 + 4.405405405

Reorder the terms:
-4.405405405 + 4.405405405 + -0.4864864865x + x2 = 0 + 4.405405405

Combine like terms: -4.405405405 + 4.405405405 = 0.000000000
0.000000000 + -0.4864864865x + x2 = 0 + 4.405405405
-0.4864864865x + x2 = 0 + 4.405405405

Combine like terms: 0 + 4.405405405 = 4.405405405
-0.4864864865x + x2 = 4.405405405

The x term is -0.4864864865x.  Take half its coefficient (-0.2432432433).
Square it (0.05916727541) and add it to both sides.

Add '0.05916727541' to each side of the equation.
-0.4864864865x + 0.05916727541 + x2 = 4.405405405 + 0.05916727541

Reorder the terms:
0.05916727541 + -0.4864864865x + x2 = 4.405405405 + 0.05916727541

Combine like terms: 4.405405405 + 0.05916727541 = 4.46457268041
0.05916727541 + -0.4864864865x + x2 = 4.46457268041

Factor a perfect square on the left side:
(x + -0.2432432433)(x + -0.2432432433) = 4.46457268041

Calculate the square root of the right side: 2.112953544

Break this problem into two subproblems by setting 
(x + -0.2432432433) equal to 2.112953544 and -2.112953544.

Subproblem 1

x + -0.2432432433 = 2.112953544 Simplifying x + -0.2432432433 = 2.112953544 Reorder the terms: -0.2432432433 + x = 2.112953544 Solving -0.2432432433 + x = 2.112953544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2432432433' to each side of the equation. -0.2432432433 + 0.2432432433 + x = 2.112953544 + 0.2432432433 Combine like terms: -0.2432432433 + 0.2432432433 = 0.0000000000 0.0000000000 + x = 2.112953544 + 0.2432432433 x = 2.112953544 + 0.2432432433 Combine like terms: 2.112953544 + 0.2432432433 = 2.3561967873 x = 2.3561967873 Simplifying x = 2.3561967873

Subproblem 2

x + -0.2432432433 = -2.112953544 Simplifying x + -0.2432432433 = -2.112953544 Reorder the terms: -0.2432432433 + x = -2.112953544 Solving -0.2432432433 + x = -2.112953544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2432432433' to each side of the equation. -0.2432432433 + 0.2432432433 + x = -2.112953544 + 0.2432432433 Combine like terms: -0.2432432433 + 0.2432432433 = 0.0000000000 0.0000000000 + x = -2.112953544 + 0.2432432433 x = -2.112953544 + 0.2432432433 Combine like terms: -2.112953544 + 0.2432432433 = -1.8697103007 x = -1.8697103007 Simplifying x = -1.8697103007

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.3561967873, -1.8697103007}

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