2a^2-12a+15=0

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Solution for 2a^2-12a+15=0 equation:


Simplifying
2a2 + -12a + 15 = 0

Reorder the terms:
15 + -12a + 2a2 = 0

Solving
15 + -12a + 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'.
7.5 + -6a + a2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + -6a + -7.5 + a2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + -6a + a2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -6a + a2 = 0 + -7.5
-6a + a2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
-6a + a2 = -7.5

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -7.5 + 9

Reorder the terms:
9 + -6a + a2 = -7.5 + 9

Combine like terms: -7.5 + 9 = 1.5
9 + -6a + a2 = 1.5

Factor a perfect square on the left side:
(a + -3)(a + -3) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(a + -3) equal to 1.224744871 and -1.224744871.

Subproblem 1

a + -3 = 1.224744871 Simplifying a + -3 = 1.224744871 Reorder the terms: -3 + a = 1.224744871 Solving -3 + a = 1.224744871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + a = 1.224744871 + 3 a = 1.224744871 + 3 Combine like terms: 1.224744871 + 3 = 4.224744871 a = 4.224744871 Simplifying a = 4.224744871

Subproblem 2

a + -3 = -1.224744871 Simplifying a + -3 = -1.224744871 Reorder the terms: -3 + a = -1.224744871 Solving -3 + a = -1.224744871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + a = -1.224744871 + 3 a = -1.224744871 + 3 Combine like terms: -1.224744871 + 3 = 1.775255129 a = 1.775255129 Simplifying a = 1.775255129

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.224744871, 1.775255129}

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