(12x^2-3x-8)-(4x^2+5)=

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Solution for (12x^2-3x-8)-(4x^2+5)= equation:


Simplifying
(12x2 + -3x + -8) + -1(4x2 + 5) = 0

Reorder the terms:
(-8 + -3x + 12x2) + -1(4x2 + 5) = 0

Remove parenthesis around (-8 + -3x + 12x2)
-8 + -3x + 12x2 + -1(4x2 + 5) = 0

Reorder the terms:
-8 + -3x + 12x2 + -1(5 + 4x2) = 0
-8 + -3x + 12x2 + (5 * -1 + 4x2 * -1) = 0
-8 + -3x + 12x2 + (-5 + -4x2) = 0

Reorder the terms:
-8 + -5 + -3x + 12x2 + -4x2 = 0

Combine like terms: -8 + -5 = -13
-13 + -3x + 12x2 + -4x2 = 0

Combine like terms: 12x2 + -4x2 = 8x2
-13 + -3x + 8x2 = 0

Solving
-13 + -3x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.625 + -0.375x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -0.375x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -0.375x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -0.375x + x2 = 0 + 1.625
-0.375x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-0.375x + x2 = 1.625

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 1.625 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 1.625 + 0.03515625

Combine like terms: 1.625 + 0.03515625 = 1.66015625
0.03515625 + -0.375x + x2 = 1.66015625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 1.66015625

Calculate the square root of the right side: 1.288470508

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 1.288470508 and -1.288470508.

Subproblem 1

x + -0.1875 = 1.288470508 Simplifying x + -0.1875 = 1.288470508 Reorder the terms: -0.1875 + x = 1.288470508 Solving -0.1875 + x = 1.288470508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.288470508 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.288470508 + 0.1875 x = 1.288470508 + 0.1875 Combine like terms: 1.288470508 + 0.1875 = 1.475970508 x = 1.475970508 Simplifying x = 1.475970508

Subproblem 2

x + -0.1875 = -1.288470508 Simplifying x + -0.1875 = -1.288470508 Reorder the terms: -0.1875 + x = -1.288470508 Solving -0.1875 + x = -1.288470508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.288470508 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.288470508 + 0.1875 x = -1.288470508 + 0.1875 Combine like terms: -1.288470508 + 0.1875 = -1.100970508 x = -1.100970508 Simplifying x = -1.100970508

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.475970508, -1.100970508}

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