a^2-40a+218=0

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Solution for a^2-40a+218=0 equation:


Simplifying
a2 + -40a + 218 = 0

Reorder the terms:
218 + -40a + a2 = 0

Solving
218 + -40a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-218' to each side of the equation.
218 + -40a + -218 + a2 = 0 + -218

Reorder the terms:
218 + -218 + -40a + a2 = 0 + -218

Combine like terms: 218 + -218 = 0
0 + -40a + a2 = 0 + -218
-40a + a2 = 0 + -218

Combine like terms: 0 + -218 = -218
-40a + a2 = -218

The a term is -40a.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40a + 400 + a2 = -218 + 400

Reorder the terms:
400 + -40a + a2 = -218 + 400

Combine like terms: -218 + 400 = 182
400 + -40a + a2 = 182

Factor a perfect square on the left side:
(a + -20)(a + -20) = 182

Calculate the square root of the right side: 13.490737563

Break this problem into two subproblems by setting 
(a + -20) equal to 13.490737563 and -13.490737563.

Subproblem 1

a + -20 = 13.490737563 Simplifying a + -20 = 13.490737563 Reorder the terms: -20 + a = 13.490737563 Solving -20 + a = 13.490737563 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = 13.490737563 + 20 Combine like terms: -20 + 20 = 0 0 + a = 13.490737563 + 20 a = 13.490737563 + 20 Combine like terms: 13.490737563 + 20 = 33.490737563 a = 33.490737563 Simplifying a = 33.490737563

Subproblem 2

a + -20 = -13.490737563 Simplifying a + -20 = -13.490737563 Reorder the terms: -20 + a = -13.490737563 Solving -20 + a = -13.490737563 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = -13.490737563 + 20 Combine like terms: -20 + 20 = 0 0 + a = -13.490737563 + 20 a = -13.490737563 + 20 Combine like terms: -13.490737563 + 20 = 6.509262437 a = 6.509262437 Simplifying a = 6.509262437

Solution

The solution to the problem is based on the solutions from the subproblems. a = {33.490737563, 6.509262437}

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