3x^2=15x-2

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Solution for 3x^2=15x-2 equation:


Simplifying
3x2 = 15x + -2

Reorder the terms:
3x2 = -2 + 15x

Solving
3x2 = -2 + 15x

Solving for variable 'x'.

Reorder the terms:
2 + -15x + 3x2 = -2 + 15x + 2 + -15x

Reorder the terms:
2 + -15x + 3x2 = -2 + 2 + 15x + -15x

Combine like terms: -2 + 2 = 0
2 + -15x + 3x2 = 0 + 15x + -15x
2 + -15x + 3x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
2 + -15x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -5x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -5x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -5x + x2 = 0 + -0.6666666667
-5x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-5x + x2 = -0.6666666667

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -0.6666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -0.6666666667 + 6.25

Combine like terms: -0.6666666667 + 6.25 = 5.5833333333
6.25 + -5x + x2 = 5.5833333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.5833333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.362907813 and -2.362907813.

Subproblem 1

x + -2.5 = 2.362907813 Simplifying x + -2.5 = 2.362907813 Reorder the terms: -2.5 + x = 2.362907813 Solving -2.5 + x = 2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.362907813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.362907813 + 2.5 x = 2.362907813 + 2.5 Combine like terms: 2.362907813 + 2.5 = 4.862907813 x = 4.862907813 Simplifying x = 4.862907813

Subproblem 2

x + -2.5 = -2.362907813 Simplifying x + -2.5 = -2.362907813 Reorder the terms: -2.5 + x = -2.362907813 Solving -2.5 + x = -2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.362907813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.362907813 + 2.5 x = -2.362907813 + 2.5 Combine like terms: -2.362907813 + 2.5 = 0.137092187 x = 0.137092187 Simplifying x = 0.137092187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.862907813, 0.137092187}

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