19a(a-6)=69

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Solution for 19a(a-6)=69 equation:


Simplifying
19a(a + -6) = 69

Reorder the terms:
19a(-6 + a) = 69
(-6 * 19a + a * 19a) = 69
(-114a + 19a2) = 69

Solving
-114a + 19a2 = 69

Solving for variable 'a'.

Reorder the terms:
-69 + -114a + 19a2 = 69 + -69

Combine like terms: 69 + -69 = 0
-69 + -114a + 19a2 = 0

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

Divide each side by '19'.
-3.631578947 + -6a + a2 = 0

Move the constant term to the right:

Add '3.631578947' to each side of the equation.
-3.631578947 + -6a + 3.631578947 + a2 = 0 + 3.631578947

Reorder the terms:
-3.631578947 + 3.631578947 + -6a + a2 = 0 + 3.631578947

Combine like terms: -3.631578947 + 3.631578947 = 0.000000000
0.000000000 + -6a + a2 = 0 + 3.631578947
-6a + a2 = 0 + 3.631578947

Combine like terms: 0 + 3.631578947 = 3.631578947
-6a + a2 = 3.631578947

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 = 3.631578947 + 9

Reorder the terms:
9 + -6a + a2 = 3.631578947 + 9

Combine like terms: 3.631578947 + 9 = 12.631578947
9 + -6a + a2 = 12.631578947

Factor a perfect square on the left side:
(a + -3)(a + -3) = 12.631578947

Calculate the square root of the right side: 3.554093267

Break this problem into two subproblems by setting 
(a + -3) equal to 3.554093267 and -3.554093267.

Subproblem 1

a + -3 = 3.554093267 Simplifying a + -3 = 3.554093267 Reorder the terms: -3 + a = 3.554093267 Solving -3 + a = 3.554093267 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 = 3.554093267 + 3 Combine like terms: -3 + 3 = 0 0 + a = 3.554093267 + 3 a = 3.554093267 + 3 Combine like terms: 3.554093267 + 3 = 6.554093267 a = 6.554093267 Simplifying a = 6.554093267

Subproblem 2

a + -3 = -3.554093267 Simplifying a + -3 = -3.554093267 Reorder the terms: -3 + a = -3.554093267 Solving -3 + a = -3.554093267 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 = -3.554093267 + 3 Combine like terms: -3 + 3 = 0 0 + a = -3.554093267 + 3 a = -3.554093267 + 3 Combine like terms: -3.554093267 + 3 = -0.554093267 a = -0.554093267 Simplifying a = -0.554093267

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.554093267, -0.554093267}

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