3a^2+100a-81600=0

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Solution for 3a^2+100a-81600=0 equation:


Simplifying
3a2 + 100a + -81600 = 0

Reorder the terms:
-81600 + 100a + 3a2 = 0

Solving
-81600 + 100a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-27200 + 33.33333333a + a2 = 0

Move the constant term to the right:

Add '27200' to each side of the equation.
-27200 + 33.33333333a + 27200 + a2 = 0 + 27200

Reorder the terms:
-27200 + 27200 + 33.33333333a + a2 = 0 + 27200

Combine like terms: -27200 + 27200 = 0
0 + 33.33333333a + a2 = 0 + 27200
33.33333333a + a2 = 0 + 27200

Combine like terms: 0 + 27200 = 27200
33.33333333a + a2 = 27200

The a term is 33.33333333a.  Take half its coefficient (16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
33.33333333a + 277.7777779 + a2 = 27200 + 277.7777779

Reorder the terms:
277.7777779 + 33.33333333a + a2 = 27200 + 277.7777779

Combine like terms: 27200 + 277.7777779 = 27477.7777779
277.7777779 + 33.33333333a + a2 = 27477.7777779

Factor a perfect square on the left side:
(a + 16.66666667)(a + 16.66666667) = 27477.7777779

Calculate the square root of the right side: 165.764223456

Break this problem into two subproblems by setting 
(a + 16.66666667) equal to 165.764223456 and -165.764223456.

Subproblem 1

a + 16.66666667 = 165.764223456 Simplifying a + 16.66666667 = 165.764223456 Reorder the terms: 16.66666667 + a = 165.764223456 Solving 16.66666667 + a = 165.764223456 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + a = 165.764223456 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + a = 165.764223456 + -16.66666667 a = 165.764223456 + -16.66666667 Combine like terms: 165.764223456 + -16.66666667 = 149.097556786 a = 149.097556786 Simplifying a = 149.097556786

Subproblem 2

a + 16.66666667 = -165.764223456 Simplifying a + 16.66666667 = -165.764223456 Reorder the terms: 16.66666667 + a = -165.764223456 Solving 16.66666667 + a = -165.764223456 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + a = -165.764223456 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + a = -165.764223456 + -16.66666667 a = -165.764223456 + -16.66666667 Combine like terms: -165.764223456 + -16.66666667 = -182.430890126 a = -182.430890126 Simplifying a = -182.430890126

Solution

The solution to the problem is based on the solutions from the subproblems. a = {149.097556786, -182.430890126}

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