(3x^2-x-5)-(x+2)=

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


Simplifying
(3x2 + -1x + -5) + -1(x + 2) = 0

Reorder the terms:
(-5 + -1x + 3x2) + -1(x + 2) = 0

Remove parenthesis around (-5 + -1x + 3x2)
-5 + -1x + 3x2 + -1(x + 2) = 0

Reorder the terms:
-5 + -1x + 3x2 + -1(2 + x) = 0
-5 + -1x + 3x2 + (2 * -1 + x * -1) = 0
-5 + -1x + 3x2 + (-2 + -1x) = 0

Reorder the terms:
-5 + -2 + -1x + -1x + 3x2 = 0

Combine like terms: -5 + -2 = -7
-7 + -1x + -1x + 3x2 = 0

Combine like terms: -1x + -1x = -2x
-7 + -2x + 3x2 = 0

Solving
-7 + -2x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.333333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -0.6666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -0.6666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 2.333333333
-0.6666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-0.6666666667x + x2 = 2.333333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 2.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 2.333333333 + 0.1111111112

Combine like terms: 2.333333333 + 0.1111111112 = 2.4444444442
0.1111111112 + -0.6666666667x + x2 = 2.4444444442

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 2.4444444442

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.56347192 and -1.56347192.

Subproblem 1

x + -0.3333333334 = 1.56347192 Simplifying x + -0.3333333334 = 1.56347192 Reorder the terms: -0.3333333334 + x = 1.56347192 Solving -0.3333333334 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 1.56347192 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.56347192 + 0.3333333334 x = 1.56347192 + 0.3333333334 Combine like terms: 1.56347192 + 0.3333333334 = 1.8968052534 x = 1.8968052534 Simplifying x = 1.8968052534

Subproblem 2

x + -0.3333333334 = -1.56347192 Simplifying x + -0.3333333334 = -1.56347192 Reorder the terms: -0.3333333334 + x = -1.56347192 Solving -0.3333333334 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -1.56347192 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.56347192 + 0.3333333334 x = -1.56347192 + 0.3333333334 Combine like terms: -1.56347192 + 0.3333333334 = -1.2301385866 x = -1.2301385866 Simplifying x = -1.2301385866

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8968052534, -1.2301385866}

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