a^2-19a+30=0

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Solution for a^2-19a+30=0 equation:


Simplifying
a2 + -19a + 30 = 0

Reorder the terms:
30 + -19a + a2 = 0

Solving
30 + -19a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -19a + -30 + a2 = 0 + -30

Reorder the terms:
30 + -30 + -19a + a2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -19a + a2 = 0 + -30
-19a + a2 = 0 + -30

Combine like terms: 0 + -30 = -30
-19a + a2 = -30

The a term is -19a.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19a + 90.25 + a2 = -30 + 90.25

Reorder the terms:
90.25 + -19a + a2 = -30 + 90.25

Combine like terms: -30 + 90.25 = 60.25
90.25 + -19a + a2 = 60.25

Factor a perfect square on the left side:
(a + -9.5)(a + -9.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(a + -9.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

a + -9.5 = 7.762087348 Simplifying a + -9.5 = 7.762087348 Reorder the terms: -9.5 + a = 7.762087348 Solving -9.5 + a = 7.762087348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + a = 7.762087348 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + a = 7.762087348 + 9.5 a = 7.762087348 + 9.5 Combine like terms: 7.762087348 + 9.5 = 17.262087348 a = 17.262087348 Simplifying a = 17.262087348

Subproblem 2

a + -9.5 = -7.762087348 Simplifying a + -9.5 = -7.762087348 Reorder the terms: -9.5 + a = -7.762087348 Solving -9.5 + a = -7.762087348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + a = -7.762087348 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + a = -7.762087348 + 9.5 a = -7.762087348 + 9.5 Combine like terms: -7.762087348 + 9.5 = 1.737912652 a = 1.737912652 Simplifying a = 1.737912652

Solution

The solution to the problem is based on the solutions from the subproblems. a = {17.262087348, 1.737912652}

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