14a^2+9a-207=0

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Solution for 14a^2+9a-207=0 equation:


Simplifying
14a2 + 9a + -207 = 0

Reorder the terms:
-207 + 9a + 14a2 = 0

Solving
-207 + 9a + 14a2 = 0

Solving for variable 'a'.

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

Divide each side by '14'.
-14.78571429 + 0.6428571429a + a2 = 0

Move the constant term to the right:

Add '14.78571429' to each side of the equation.
-14.78571429 + 0.6428571429a + 14.78571429 + a2 = 0 + 14.78571429

Reorder the terms:
-14.78571429 + 14.78571429 + 0.6428571429a + a2 = 0 + 14.78571429

Combine like terms: -14.78571429 + 14.78571429 = 0.00000000
0.00000000 + 0.6428571429a + a2 = 0 + 14.78571429
0.6428571429a + a2 = 0 + 14.78571429

Combine like terms: 0 + 14.78571429 = 14.78571429
0.6428571429a + a2 = 14.78571429

The a term is 0.6428571429a.  Take half its coefficient (0.3214285715).
Square it (0.1033163266) and add it to both sides.

Add '0.1033163266' to each side of the equation.
0.6428571429a + 0.1033163266 + a2 = 14.78571429 + 0.1033163266

Reorder the terms:
0.1033163266 + 0.6428571429a + a2 = 14.78571429 + 0.1033163266

Combine like terms: 14.78571429 + 0.1033163266 = 14.8890306166
0.1033163266 + 0.6428571429a + a2 = 14.8890306166

Factor a perfect square on the left side:
(a + 0.3214285715)(a + 0.3214285715) = 14.8890306166

Calculate the square root of the right side: 3.858630666

Break this problem into two subproblems by setting 
(a + 0.3214285715) equal to 3.858630666 and -3.858630666.

Subproblem 1

a + 0.3214285715 = 3.858630666 Simplifying a + 0.3214285715 = 3.858630666 Reorder the terms: 0.3214285715 + a = 3.858630666 Solving 0.3214285715 + a = 3.858630666 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3214285715' to each side of the equation. 0.3214285715 + -0.3214285715 + a = 3.858630666 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + a = 3.858630666 + -0.3214285715 a = 3.858630666 + -0.3214285715 Combine like terms: 3.858630666 + -0.3214285715 = 3.5372020945 a = 3.5372020945 Simplifying a = 3.5372020945

Subproblem 2

a + 0.3214285715 = -3.858630666 Simplifying a + 0.3214285715 = -3.858630666 Reorder the terms: 0.3214285715 + a = -3.858630666 Solving 0.3214285715 + a = -3.858630666 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3214285715' to each side of the equation. 0.3214285715 + -0.3214285715 + a = -3.858630666 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + a = -3.858630666 + -0.3214285715 a = -3.858630666 + -0.3214285715 Combine like terms: -3.858630666 + -0.3214285715 = -4.1800592375 a = -4.1800592375 Simplifying a = -4.1800592375

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.5372020945, -4.1800592375}

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