56a^2+1215a+45=0

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Solution for 56a^2+1215a+45=0 equation:


Simplifying
56a2 + 1215a + 45 = 0

Reorder the terms:
45 + 1215a + 56a2 = 0

Solving
45 + 1215a + 56a2 = 0

Solving for variable 'a'.

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

Divide each side by '56'.
0.8035714286 + 21.69642857a + a2 = 0

Move the constant term to the right:

Add '-0.8035714286' to each side of the equation.
0.8035714286 + 21.69642857a + -0.8035714286 + a2 = 0 + -0.8035714286

Reorder the terms:
0.8035714286 + -0.8035714286 + 21.69642857a + a2 = 0 + -0.8035714286

Combine like terms: 0.8035714286 + -0.8035714286 = 0.0000000000
0.0000000000 + 21.69642857a + a2 = 0 + -0.8035714286
21.69642857a + a2 = 0 + -0.8035714286

Combine like terms: 0 + -0.8035714286 = -0.8035714286
21.69642857a + a2 = -0.8035714286

The a term is 21.69642857a.  Take half its coefficient (10.84821429).
Square it (117.6837533) and add it to both sides.

Add '117.6837533' to each side of the equation.
21.69642857a + 117.6837533 + a2 = -0.8035714286 + 117.6837533

Reorder the terms:
117.6837533 + 21.69642857a + a2 = -0.8035714286 + 117.6837533

Combine like terms: -0.8035714286 + 117.6837533 = 116.8801818714
117.6837533 + 21.69642857a + a2 = 116.8801818714

Factor a perfect square on the left side:
(a + 10.84821429)(a + 10.84821429) = 116.8801818714

Calculate the square root of the right side: 10.811113813

Break this problem into two subproblems by setting 
(a + 10.84821429) equal to 10.811113813 and -10.811113813.

Subproblem 1

a + 10.84821429 = 10.811113813 Simplifying a + 10.84821429 = 10.811113813 Reorder the terms: 10.84821429 + a = 10.811113813 Solving 10.84821429 + a = 10.811113813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10.84821429' to each side of the equation. 10.84821429 + -10.84821429 + a = 10.811113813 + -10.84821429 Combine like terms: 10.84821429 + -10.84821429 = 0.00000000 0.00000000 + a = 10.811113813 + -10.84821429 a = 10.811113813 + -10.84821429 Combine like terms: 10.811113813 + -10.84821429 = -0.037100477 a = -0.037100477 Simplifying a = -0.037100477

Subproblem 2

a + 10.84821429 = -10.811113813 Simplifying a + 10.84821429 = -10.811113813 Reorder the terms: 10.84821429 + a = -10.811113813 Solving 10.84821429 + a = -10.811113813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10.84821429' to each side of the equation. 10.84821429 + -10.84821429 + a = -10.811113813 + -10.84821429 Combine like terms: 10.84821429 + -10.84821429 = 0.00000000 0.00000000 + a = -10.811113813 + -10.84821429 a = -10.811113813 + -10.84821429 Combine like terms: -10.811113813 + -10.84821429 = -21.659328103 a = -21.659328103 Simplifying a = -21.659328103

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.037100477, -21.659328103}

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