5x^2-12x+2=0

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Solution for 5x^2-12x+2=0 equation:


Simplifying
5x2 + -12x + 2 = 0

Reorder the terms:
2 + -12x + 5x2 = 0

Solving
2 + -12x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.4 + -2.4x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2.4x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2.4x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2.4x + x2 = 0 + -0.4
-2.4x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2.4x + x2 = -0.4

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = -0.4 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = -0.4 + 1.44

Combine like terms: -0.4 + 1.44 = 1.04
1.44 + -2.4x + x2 = 1.04

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 1.04

Calculate the square root of the right side: 1.019803903

Break this problem into two subproblems by setting 
(x + -1.2) equal to 1.019803903 and -1.019803903.

Subproblem 1

x + -1.2 = 1.019803903 Simplifying x + -1.2 = 1.019803903 Reorder the terms: -1.2 + x = 1.019803903 Solving -1.2 + x = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.019803903 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.019803903 + 1.2 x = 1.019803903 + 1.2 Combine like terms: 1.019803903 + 1.2 = 2.219803903 x = 2.219803903 Simplifying x = 2.219803903

Subproblem 2

x + -1.2 = -1.019803903 Simplifying x + -1.2 = -1.019803903 Reorder the terms: -1.2 + x = -1.019803903 Solving -1.2 + x = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.019803903 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.019803903 + 1.2 x = -1.019803903 + 1.2 Combine like terms: -1.019803903 + 1.2 = 0.180196097 x = 0.180196097 Simplifying x = 0.180196097

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.219803903, 0.180196097}

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