351=-.5x^2+36x-171

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Solution for 351=-.5x^2+36x-171 equation:


Simplifying
351 = -0.5x2 + 36x + -171

Reorder the terms:
351 = -171 + 36x + -0.5x2

Solving
351 = -171 + 36x + -0.5x2

Solving for variable 'x'.

Combine like terms: 351 + 171 = 522
522 + -36x + 0.5x2 = -171 + 36x + -0.5x2 + 171 + -36x + 0.5x2

Reorder the terms:
522 + -36x + 0.5x2 = -171 + 171 + 36x + -36x + -0.5x2 + 0.5x2

Combine like terms: -171 + 171 = 0
522 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2
522 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2

Combine like terms: 36x + -36x = 0
522 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2
522 + -36x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
522 + -36x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
1044 + -72x + x2 = 0

Move the constant term to the right:

Add '-1044' to each side of the equation.
1044 + -72x + -1044 + x2 = 0 + -1044

Reorder the terms:
1044 + -1044 + -72x + x2 = 0 + -1044

Combine like terms: 1044 + -1044 = 0
0 + -72x + x2 = 0 + -1044
-72x + x2 = 0 + -1044

Combine like terms: 0 + -1044 = -1044
-72x + x2 = -1044

The x term is -72x.  Take half its coefficient (-36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
-72x + 1296 + x2 = -1044 + 1296

Reorder the terms:
1296 + -72x + x2 = -1044 + 1296

Combine like terms: -1044 + 1296 = 252
1296 + -72x + x2 = 252

Factor a perfect square on the left side:
(x + -36)(x + -36) = 252

Calculate the square root of the right side: 15.874507866

Break this problem into two subproblems by setting 
(x + -36) equal to 15.874507866 and -15.874507866.

Subproblem 1

x + -36 = 15.874507866 Simplifying x + -36 = 15.874507866 Reorder the terms: -36 + x = 15.874507866 Solving -36 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 15.874507866 + 36 Combine like terms: -36 + 36 = 0 0 + x = 15.874507866 + 36 x = 15.874507866 + 36 Combine like terms: 15.874507866 + 36 = 51.874507866 x = 51.874507866 Simplifying x = 51.874507866

Subproblem 2

x + -36 = -15.874507866 Simplifying x + -36 = -15.874507866 Reorder the terms: -36 + x = -15.874507866 Solving -36 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -15.874507866 + 36 Combine like terms: -36 + 36 = 0 0 + x = -15.874507866 + 36 x = -15.874507866 + 36 Combine like terms: -15.874507866 + 36 = 20.125492134 x = 20.125492134 Simplifying x = 20.125492134

Solution

The solution to the problem is based on the solutions from the subproblems. x = {51.874507866, 20.125492134}

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