12x^2-9x-10=0

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


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

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

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

Solving for variable 'x'.

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

Divide each side by '12'.
-0.8333333333 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -0.75x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -0.75x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -0.75x + x2 = 0 + 0.8333333333
-0.75x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-0.75x + x2 = 0.8333333333

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.8333333333 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.8333333333 + 0.140625

Combine like terms: 0.8333333333 + 0.140625 = 0.9739583333
0.140625 + -0.75x + x2 = 0.9739583333

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.9739583333

Calculate the square root of the right side: 0.986893274

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.986893274 and -0.986893274.

Subproblem 1

x + -0.375 = 0.986893274 Simplifying x + -0.375 = 0.986893274 Reorder the terms: -0.375 + x = 0.986893274 Solving -0.375 + x = 0.986893274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.986893274 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.986893274 + 0.375 x = 0.986893274 + 0.375 Combine like terms: 0.986893274 + 0.375 = 1.361893274 x = 1.361893274 Simplifying x = 1.361893274

Subproblem 2

x + -0.375 = -0.986893274 Simplifying x + -0.375 = -0.986893274 Reorder the terms: -0.375 + x = -0.986893274 Solving -0.375 + x = -0.986893274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.986893274 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.986893274 + 0.375 x = -0.986893274 + 0.375 Combine like terms: -0.986893274 + 0.375 = -0.611893274 x = -0.611893274 Simplifying x = -0.611893274

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.361893274, -0.611893274}

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