9a^2-25a-16=0

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Solution for 9a^2-25a-16=0 equation:


Simplifying
9a2 + -25a + -16 = 0

Reorder the terms:
-16 + -25a + 9a2 = 0

Solving
-16 + -25a + 9a2 = 0

Solving for variable 'a'.

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

Divide each side by '9'.
-1.777777778 + -2.777777778a + a2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -2.777777778a + 1.777777778 + a2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -2.777777778a + a2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -2.777777778a + a2 = 0 + 1.777777778
-2.777777778a + a2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-2.777777778a + a2 = 1.777777778

The a term is -2.777777778a.  Take half its coefficient (-1.388888889).
Square it (1.929012346) and add it to both sides.

Add '1.929012346' to each side of the equation.
-2.777777778a + 1.929012346 + a2 = 1.777777778 + 1.929012346

Reorder the terms:
1.929012346 + -2.777777778a + a2 = 1.777777778 + 1.929012346

Combine like terms: 1.777777778 + 1.929012346 = 3.706790124
1.929012346 + -2.777777778a + a2 = 3.706790124

Factor a perfect square on the left side:
(a + -1.388888889)(a + -1.388888889) = 3.706790124

Calculate the square root of the right side: 1.925302606

Break this problem into two subproblems by setting 
(a + -1.388888889) equal to 1.925302606 and -1.925302606.

Subproblem 1

a + -1.388888889 = 1.925302606 Simplifying a + -1.388888889 = 1.925302606 Reorder the terms: -1.388888889 + a = 1.925302606 Solving -1.388888889 + a = 1.925302606 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + a = 1.925302606 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + a = 1.925302606 + 1.388888889 a = 1.925302606 + 1.388888889 Combine like terms: 1.925302606 + 1.388888889 = 3.314191495 a = 3.314191495 Simplifying a = 3.314191495

Subproblem 2

a + -1.388888889 = -1.925302606 Simplifying a + -1.388888889 = -1.925302606 Reorder the terms: -1.388888889 + a = -1.925302606 Solving -1.388888889 + a = -1.925302606 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + a = -1.925302606 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + a = -1.925302606 + 1.388888889 a = -1.925302606 + 1.388888889 Combine like terms: -1.925302606 + 1.388888889 = -0.536413717 a = -0.536413717 Simplifying a = -0.536413717

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.314191495, -0.536413717}

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