3x^2-15x+5=0

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Solution for 3x^2-15x+5=0 equation:


Simplifying
3x2 + -15x + 5 = 0

Reorder the terms:
5 + -15x + 3x2 = 0

Solving
5 + -15x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
1.666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -5x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -5x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + -1.666666667
-5x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-5x + x2 = -1.666666667

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 = -1.666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1.666666667 + 6.25

Combine like terms: -1.666666667 + 6.25 = 4.583333333
6.25 + -5x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.140872096 and -2.140872096.

Subproblem 1

x + -2.5 = 2.140872096 Simplifying x + -2.5 = 2.140872096 Reorder the terms: -2.5 + x = 2.140872096 Solving -2.5 + x = 2.140872096 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 = 2.140872096 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.140872096 + 2.5 x = 2.140872096 + 2.5 Combine like terms: 2.140872096 + 2.5 = 4.640872096 x = 4.640872096 Simplifying x = 4.640872096

Subproblem 2

x + -2.5 = -2.140872096 Simplifying x + -2.5 = -2.140872096 Reorder the terms: -2.5 + x = -2.140872096 Solving -2.5 + x = -2.140872096 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 = -2.140872096 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.140872096 + 2.5 x = -2.140872096 + 2.5 Combine like terms: -2.140872096 + 2.5 = 0.359127904 x = 0.359127904 Simplifying x = 0.359127904

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.640872096, 0.359127904}

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