3x^2+13x-28=2x+2

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Solution for 3x^2+13x-28=2x+2 equation:


Simplifying
3x2 + 13x + -28 = 2x + 2

Reorder the terms:
-28 + 13x + 3x2 = 2x + 2

Reorder the terms:
-28 + 13x + 3x2 = 2 + 2x

Solving
-28 + 13x + 3x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-28 + -2 + 13x + -2x + 3x2 = 2 + 2x + -2 + -2x

Combine like terms: -28 + -2 = -30
-30 + 13x + -2x + 3x2 = 2 + 2x + -2 + -2x

Combine like terms: 13x + -2x = 11x
-30 + 11x + 3x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-30 + 11x + 3x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-30 + 11x + 3x2 = 0 + 2x + -2x
-30 + 11x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-30 + 11x + 3x2 = 0

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

Divide each side by '3'.
-10 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 3.666666667x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 3.666666667x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3.666666667x + x2 = 0 + 10
3.666666667x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
3.666666667x + x2 = 10

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 10 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 10 + 3.361111114

Combine like terms: 10 + 3.361111114 = 13.361111114
3.361111114 + 3.666666667x + x2 = 13.361111114

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 13.361111114

Calculate the square root of the right side: 3.655285367

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 3.655285367 and -3.655285367.

Subproblem 1

x + 1.833333334 = 3.655285367 Simplifying x + 1.833333334 = 3.655285367 Reorder the terms: 1.833333334 + x = 3.655285367 Solving 1.833333334 + x = 3.655285367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 3.655285367 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 3.655285367 + -1.833333334 x = 3.655285367 + -1.833333334 Combine like terms: 3.655285367 + -1.833333334 = 1.821952033 x = 1.821952033 Simplifying x = 1.821952033

Subproblem 2

x + 1.833333334 = -3.655285367 Simplifying x + 1.833333334 = -3.655285367 Reorder the terms: 1.833333334 + x = -3.655285367 Solving 1.833333334 + x = -3.655285367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -3.655285367 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -3.655285367 + -1.833333334 x = -3.655285367 + -1.833333334 Combine like terms: -3.655285367 + -1.833333334 = -5.488618701 x = -5.488618701 Simplifying x = -5.488618701

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.821952033, -5.488618701}

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