10a^2+9a-12=0

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Solution for 10a^2+9a-12=0 equation:


Simplifying
10a2 + 9a + -12 = 0

Reorder the terms:
-12 + 9a + 10a2 = 0

Solving
-12 + 9a + 10a2 = 0

Solving for variable 'a'.

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

Divide each side by '10'.
-1.2 + 0.9a + a2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 0.9a + 1.2 + a2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 0.9a + a2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 0.9a + a2 = 0 + 1.2
0.9a + a2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
0.9a + a2 = 1.2

The a term is 0.9a.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9a + 0.2025 + a2 = 1.2 + 0.2025

Reorder the terms:
0.2025 + 0.9a + a2 = 1.2 + 0.2025

Combine like terms: 1.2 + 0.2025 = 1.4025
0.2025 + 0.9a + a2 = 1.4025

Factor a perfect square on the left side:
(a + 0.45)(a + 0.45) = 1.4025

Calculate the square root of the right side: 1.184271928

Break this problem into two subproblems by setting 
(a + 0.45) equal to 1.184271928 and -1.184271928.

Subproblem 1

a + 0.45 = 1.184271928 Simplifying a + 0.45 = 1.184271928 Reorder the terms: 0.45 + a = 1.184271928 Solving 0.45 + a = 1.184271928 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + a = 1.184271928 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + a = 1.184271928 + -0.45 a = 1.184271928 + -0.45 Combine like terms: 1.184271928 + -0.45 = 0.734271928 a = 0.734271928 Simplifying a = 0.734271928

Subproblem 2

a + 0.45 = -1.184271928 Simplifying a + 0.45 = -1.184271928 Reorder the terms: 0.45 + a = -1.184271928 Solving 0.45 + a = -1.184271928 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + a = -1.184271928 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + a = -1.184271928 + -0.45 a = -1.184271928 + -0.45 Combine like terms: -1.184271928 + -0.45 = -1.634271928 a = -1.634271928 Simplifying a = -1.634271928

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.734271928, -1.634271928}

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