5x^2=6x+2

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Solution for 5x^2=6x+2 equation:


Simplifying
5x2 = 6x + 2

Reorder the terms:
5x2 = 2 + 6x

Solving
5x2 = 2 + 6x

Solving for variable 'x'.

Reorder the terms:
-2 + -6x + 5x2 = 2 + 6x + -2 + -6x

Reorder the terms:
-2 + -6x + 5x2 = 2 + -2 + 6x + -6x

Combine like terms: 2 + -2 = 0
-2 + -6x + 5x2 = 0 + 6x + -6x
-2 + -6x + 5x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + -6x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + -1.2x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1.2x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1.2x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1.2x + x2 = 0 + 0.4
-1.2x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1.2x + x2 = 0.4

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 0.4 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 0.4 + 0.36

Combine like terms: 0.4 + 0.36 = 0.76
0.36 + -1.2x + x2 = 0.76

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.871779789 and -0.871779789.

Subproblem 1

x + -0.6 = 0.871779789 Simplifying x + -0.6 = 0.871779789 Reorder the terms: -0.6 + x = 0.871779789 Solving -0.6 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.871779789 + 0.6 x = 0.871779789 + 0.6 Combine like terms: 0.871779789 + 0.6 = 1.471779789 x = 1.471779789 Simplifying x = 1.471779789

Subproblem 2

x + -0.6 = -0.871779789 Simplifying x + -0.6 = -0.871779789 Reorder the terms: -0.6 + x = -0.871779789 Solving -0.6 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.871779789 + 0.6 x = -0.871779789 + 0.6 Combine like terms: -0.871779789 + 0.6 = -0.271779789 x = -0.271779789 Simplifying x = -0.271779789

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.471779789, -0.271779789}

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