2x-3x+2=5x^2-3x-8

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Solution for 2x-3x+2=5x^2-3x-8 equation:


Simplifying
2x + -3x + 2 = 5x2 + -3x + -8

Reorder the terms:
2 + 2x + -3x = 5x2 + -3x + -8

Combine like terms: 2x + -3x = -1x
2 + -1x = 5x2 + -3x + -8

Reorder the terms:
2 + -1x = -8 + -3x + 5x2

Solving
2 + -1x = -8 + -3x + 5x2

Solving for variable 'x'.

Reorder the terms:
2 + 8 + -1x + 3x + -5x2 = -8 + -3x + 5x2 + 8 + 3x + -5x2

Combine like terms: 2 + 8 = 10
10 + -1x + 3x + -5x2 = -8 + -3x + 5x2 + 8 + 3x + -5x2

Combine like terms: -1x + 3x = 2x
10 + 2x + -5x2 = -8 + -3x + 5x2 + 8 + 3x + -5x2

Reorder the terms:
10 + 2x + -5x2 = -8 + 8 + -3x + 3x + 5x2 + -5x2

Combine like terms: -8 + 8 = 0
10 + 2x + -5x2 = 0 + -3x + 3x + 5x2 + -5x2
10 + 2x + -5x2 = -3x + 3x + 5x2 + -5x2

Combine like terms: -3x + 3x = 0
10 + 2x + -5x2 = 0 + 5x2 + -5x2
10 + 2x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
10 + 2x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2 + -0.4x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.4x + x2 = 0 + 2
-0.4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.4x + x2 = 2

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 2 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 2 + 0.04

Combine like terms: 2 + 0.04 = 2.04
0.04 + -0.4x + x2 = 2.04

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 2.04

Calculate the square root of the right side: 1.428285686

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.428285686 and -1.428285686.

Subproblem 1

x + -0.2 = 1.428285686 Simplifying x + -0.2 = 1.428285686 Reorder the terms: -0.2 + x = 1.428285686 Solving -0.2 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.428285686 + 0.2 x = 1.428285686 + 0.2 Combine like terms: 1.428285686 + 0.2 = 1.628285686 x = 1.628285686 Simplifying x = 1.628285686

Subproblem 2

x + -0.2 = -1.428285686 Simplifying x + -0.2 = -1.428285686 Reorder the terms: -0.2 + x = -1.428285686 Solving -0.2 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.428285686 + 0.2 x = -1.428285686 + 0.2 Combine like terms: -1.428285686 + 0.2 = -1.228285686 x = -1.228285686 Simplifying x = -1.228285686

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.628285686, -1.228285686}

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