10x^2-9x-12=0

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


Simplifying
10x2 + -9x + -12 = 0

Reorder the terms:
-12 + -9x + 10x2 = 0

Solving
-12 + -9x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-1.2 + -0.9x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -0.9x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -0.9x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -0.9x + x2 = 0 + 1.2
-0.9x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-0.9x + x2 = 1.2

The x term is -0.9x.  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.
-0.9x + 0.2025 + x2 = 1.2 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = 1.2 + 0.2025

Combine like terms: 1.2 + 0.2025 = 1.4025
0.2025 + -0.9x + x2 = 1.4025

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

Calculate the square root of the right side: 1.184271928

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

Subproblem 1

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

Subproblem 2

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

Solution

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

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