a^2-40a+25=0

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Solution for a^2-40a+25=0 equation:


Simplifying
a2 + -40a + 25 = 0

Reorder the terms:
25 + -40a + a2 = 0

Solving
25 + -40a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -40a + -25 + a2 = 0 + -25

Reorder the terms:
25 + -25 + -40a + a2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -40a + a2 = 0 + -25
-40a + a2 = 0 + -25

Combine like terms: 0 + -25 = -25
-40a + a2 = -25

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 = -25 + 400

Reorder the terms:
400 + -40a + a2 = -25 + 400

Combine like terms: -25 + 400 = 375
400 + -40a + a2 = 375

Factor a perfect square on the left side:
(a + -20)(a + -20) = 375

Calculate the square root of the right side: 19.364916731

Break this problem into two subproblems by setting 
(a + -20) equal to 19.364916731 and -19.364916731.

Subproblem 1

a + -20 = 19.364916731 Simplifying a + -20 = 19.364916731 Reorder the terms: -20 + a = 19.364916731 Solving -20 + a = 19.364916731 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 = 19.364916731 + 20 Combine like terms: -20 + 20 = 0 0 + a = 19.364916731 + 20 a = 19.364916731 + 20 Combine like terms: 19.364916731 + 20 = 39.364916731 a = 39.364916731 Simplifying a = 39.364916731

Subproblem 2

a + -20 = -19.364916731 Simplifying a + -20 = -19.364916731 Reorder the terms: -20 + a = -19.364916731 Solving -20 + a = -19.364916731 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 = -19.364916731 + 20 Combine like terms: -20 + 20 = 0 0 + a = -19.364916731 + 20 a = -19.364916731 + 20 Combine like terms: -19.364916731 + 20 = 0.635083269 a = 0.635083269 Simplifying a = 0.635083269

Solution

The solution to the problem is based on the solutions from the subproblems. a = {39.364916731, 0.635083269}

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