18a^2=-57a+35

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Solution for 18a^2=-57a+35 equation:


Simplifying
18a2 = -57a + 35

Reorder the terms:
18a2 = 35 + -57a

Solving
18a2 = 35 + -57a

Solving for variable 'a'.

Reorder the terms:
-35 + 57a + 18a2 = 35 + -57a + -35 + 57a

Reorder the terms:
-35 + 57a + 18a2 = 35 + -35 + -57a + 57a

Combine like terms: 35 + -35 = 0
-35 + 57a + 18a2 = 0 + -57a + 57a
-35 + 57a + 18a2 = -57a + 57a

Combine like terms: -57a + 57a = 0
-35 + 57a + 18a2 = 0

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

Divide each side by '18'.
-1.944444444 + 3.166666667a + a2 = 0

Move the constant term to the right:

Add '1.944444444' to each side of the equation.
-1.944444444 + 3.166666667a + 1.944444444 + a2 = 0 + 1.944444444

Reorder the terms:
-1.944444444 + 1.944444444 + 3.166666667a + a2 = 0 + 1.944444444

Combine like terms: -1.944444444 + 1.944444444 = 0.000000000
0.000000000 + 3.166666667a + a2 = 0 + 1.944444444
3.166666667a + a2 = 0 + 1.944444444

Combine like terms: 0 + 1.944444444 = 1.944444444
3.166666667a + a2 = 1.944444444

The a term is 3.166666667a.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667a + 2.506944447 + a2 = 1.944444444 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667a + a2 = 1.944444444 + 2.506944447

Combine like terms: 1.944444444 + 2.506944447 = 4.451388891
2.506944447 + 3.166666667a + a2 = 4.451388891

Factor a perfect square on the left side:
(a + 1.583333334)(a + 1.583333334) = 4.451388891

Calculate the square root of the right side: 2.109831484

Break this problem into two subproblems by setting 
(a + 1.583333334) equal to 2.109831484 and -2.109831484.

Subproblem 1

a + 1.583333334 = 2.109831484 Simplifying a + 1.583333334 = 2.109831484 Reorder the terms: 1.583333334 + a = 2.109831484 Solving 1.583333334 + a = 2.109831484 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + a = 2.109831484 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + a = 2.109831484 + -1.583333334 a = 2.109831484 + -1.583333334 Combine like terms: 2.109831484 + -1.583333334 = 0.52649815 a = 0.52649815 Simplifying a = 0.52649815

Subproblem 2

a + 1.583333334 = -2.109831484 Simplifying a + 1.583333334 = -2.109831484 Reorder the terms: 1.583333334 + a = -2.109831484 Solving 1.583333334 + a = -2.109831484 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + a = -2.109831484 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + a = -2.109831484 + -1.583333334 a = -2.109831484 + -1.583333334 Combine like terms: -2.109831484 + -1.583333334 = -3.693164818 a = -3.693164818 Simplifying a = -3.693164818

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.52649815, -3.693164818}

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