6a(3a-2)+5a=57

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Solution for 6a(3a-2)+5a=57 equation:


Simplifying
6a(3a + -2) + 5a = 57

Reorder the terms:
6a(-2 + 3a) + 5a = 57
(-2 * 6a + 3a * 6a) + 5a = 57
(-12a + 18a2) + 5a = 57

Reorder the terms:
-12a + 5a + 18a2 = 57

Combine like terms: -12a + 5a = -7a
-7a + 18a2 = 57

Solving
-7a + 18a2 = 57

Solving for variable 'a'.

Reorder the terms:
-57 + -7a + 18a2 = 57 + -57

Combine like terms: 57 + -57 = 0
-57 + -7a + 18a2 = 0

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

Divide each side by '18'.
-3.166666667 + -0.3888888889a + a2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + -0.3888888889a + 3.166666667 + a2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + -0.3888888889a + a2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + -0.3888888889a + a2 = 0 + 3.166666667
-0.3888888889a + a2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
-0.3888888889a + a2 = 3.166666667

The a term is -0.3888888889a.  Take half its coefficient (-0.1944444445).
Square it (0.03780864200) and add it to both sides.

Add '0.03780864200' to each side of the equation.
-0.3888888889a + 0.03780864200 + a2 = 3.166666667 + 0.03780864200

Reorder the terms:
0.03780864200 + -0.3888888889a + a2 = 3.166666667 + 0.03780864200

Combine like terms: 3.166666667 + 0.03780864200 = 3.204475309
0.03780864200 + -0.3888888889a + a2 = 3.204475309

Factor a perfect square on the left side:
(a + -0.1944444445)(a + -0.1944444445) = 3.204475309

Calculate the square root of the right side: 1.790104832

Break this problem into two subproblems by setting 
(a + -0.1944444445) equal to 1.790104832 and -1.790104832.

Subproblem 1

a + -0.1944444445 = 1.790104832 Simplifying a + -0.1944444445 = 1.790104832 Reorder the terms: -0.1944444445 + a = 1.790104832 Solving -0.1944444445 + a = 1.790104832 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + a = 1.790104832 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + a = 1.790104832 + 0.1944444445 a = 1.790104832 + 0.1944444445 Combine like terms: 1.790104832 + 0.1944444445 = 1.9845492765 a = 1.9845492765 Simplifying a = 1.9845492765

Subproblem 2

a + -0.1944444445 = -1.790104832 Simplifying a + -0.1944444445 = -1.790104832 Reorder the terms: -0.1944444445 + a = -1.790104832 Solving -0.1944444445 + a = -1.790104832 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + a = -1.790104832 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + a = -1.790104832 + 0.1944444445 a = -1.790104832 + 0.1944444445 Combine like terms: -1.790104832 + 0.1944444445 = -1.5956603875 a = -1.5956603875 Simplifying a = -1.5956603875

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.9845492765, -1.5956603875}

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