2a^2-46a+225=0

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Solution for 2a^2-46a+225=0 equation:


Simplifying
2a2 + -46a + 225 = 0

Reorder the terms:
225 + -46a + 2a2 = 0

Solving
225 + -46a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
112.5 + -23a + a2 = 0

Move the constant term to the right:

Add '-112.5' to each side of the equation.
112.5 + -23a + -112.5 + a2 = 0 + -112.5

Reorder the terms:
112.5 + -112.5 + -23a + a2 = 0 + -112.5

Combine like terms: 112.5 + -112.5 = 0.0
0.0 + -23a + a2 = 0 + -112.5
-23a + a2 = 0 + -112.5

Combine like terms: 0 + -112.5 = -112.5
-23a + a2 = -112.5

The a term is -23a.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23a + 132.25 + a2 = -112.5 + 132.25

Reorder the terms:
132.25 + -23a + a2 = -112.5 + 132.25

Combine like terms: -112.5 + 132.25 = 19.75
132.25 + -23a + a2 = 19.75

Factor a perfect square on the left side:
(a + -11.5)(a + -11.5) = 19.75

Calculate the square root of the right side: 4.444097209

Break this problem into two subproblems by setting 
(a + -11.5) equal to 4.444097209 and -4.444097209.

Subproblem 1

a + -11.5 = 4.444097209 Simplifying a + -11.5 = 4.444097209 Reorder the terms: -11.5 + a = 4.444097209 Solving -11.5 + a = 4.444097209 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + a = 4.444097209 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + a = 4.444097209 + 11.5 a = 4.444097209 + 11.5 Combine like terms: 4.444097209 + 11.5 = 15.944097209 a = 15.944097209 Simplifying a = 15.944097209

Subproblem 2

a + -11.5 = -4.444097209 Simplifying a + -11.5 = -4.444097209 Reorder the terms: -11.5 + a = -4.444097209 Solving -11.5 + a = -4.444097209 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + a = -4.444097209 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + a = -4.444097209 + 11.5 a = -4.444097209 + 11.5 Combine like terms: -4.444097209 + 11.5 = 7.055902791 a = 7.055902791 Simplifying a = 7.055902791

Solution

The solution to the problem is based on the solutions from the subproblems. a = {15.944097209, 7.055902791}

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