800a-a^2=31692.94

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Solution for 800a-a^2=31692.94 equation:


Simplifying
800a + -1a2 = 31692.94

Solving
800a + -1a2 = 31692.94

Solving for variable 'a'.

Reorder the terms:
-31692.94 + 800a + -1a2 = 31692.94 + -31692.94

Combine like terms: 31692.94 + -31692.94 = 0.00
-31692.94 + 800a + -1a2 = 0.00

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
31692.94 + -800a + a2 = 0.00

Move the constant term to the right:

Add '-31692.94' to each side of the equation.
31692.94 + -800a + -31692.94 + a2 = 0.00 + -31692.94

Reorder the terms:
31692.94 + -31692.94 + -800a + a2 = 0.00 + -31692.94

Combine like terms: 31692.94 + -31692.94 = 0.00
0.00 + -800a + a2 = 0.00 + -31692.94
-800a + a2 = 0.00 + -31692.94

Combine like terms: 0.00 + -31692.94 = -31692.94
-800a + a2 = -31692.94

The a term is -800a.  Take half its coefficient (-400).
Square it (160000) and add it to both sides.

Add '160000' to each side of the equation.
-800a + 160000 + a2 = -31692.94 + 160000

Reorder the terms:
160000 + -800a + a2 = -31692.94 + 160000

Combine like terms: -31692.94 + 160000 = 128307.06
160000 + -800a + a2 = 128307.06

Factor a perfect square on the left side:
(a + -400)(a + -400) = 128307.06

Calculate the square root of the right side: 358.199748744

Break this problem into two subproblems by setting 
(a + -400) equal to 358.199748744 and -358.199748744.

Subproblem 1

a + -400 = 358.199748744 Simplifying a + -400 = 358.199748744 Reorder the terms: -400 + a = 358.199748744 Solving -400 + a = 358.199748744 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + a = 358.199748744 + 400 Combine like terms: -400 + 400 = 0 0 + a = 358.199748744 + 400 a = 358.199748744 + 400 Combine like terms: 358.199748744 + 400 = 758.199748744 a = 758.199748744 Simplifying a = 758.199748744

Subproblem 2

a + -400 = -358.199748744 Simplifying a + -400 = -358.199748744 Reorder the terms: -400 + a = -358.199748744 Solving -400 + a = -358.199748744 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + a = -358.199748744 + 400 Combine like terms: -400 + 400 = 0 0 + a = -358.199748744 + 400 a = -358.199748744 + 400 Combine like terms: -358.199748744 + 400 = 41.800251256 a = 41.800251256 Simplifying a = 41.800251256

Solution

The solution to the problem is based on the solutions from the subproblems. a = {758.199748744, 41.800251256}

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