3x^2-15x+17=0

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Solution for 3x^2-15x+17=0 equation:


Simplifying
3x2 + -15x + 17 = 0

Reorder the terms:
17 + -15x + 3x2 = 0

Solving
17 + -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'.
5.666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -5x + -5.666666667 + x2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -5x + x2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + -5.666666667
-5x + x2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-5x + x2 = -5.666666667

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 = -5.666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5.666666667 + 6.25

Combine like terms: -5.666666667 + 6.25 = 0.583333333
6.25 + -5x + x2 = 0.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.583333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.763762616 and -0.763762616.

Subproblem 1

x + -2.5 = 0.763762616 Simplifying x + -2.5 = 0.763762616 Reorder the terms: -2.5 + x = 0.763762616 Solving -2.5 + x = 0.763762616 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 = 0.763762616 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.763762616 + 2.5 x = 0.763762616 + 2.5 Combine like terms: 0.763762616 + 2.5 = 3.263762616 x = 3.263762616 Simplifying x = 3.263762616

Subproblem 2

x + -2.5 = -0.763762616 Simplifying x + -2.5 = -0.763762616 Reorder the terms: -2.5 + x = -0.763762616 Solving -2.5 + x = -0.763762616 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 = -0.763762616 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.763762616 + 2.5 x = -0.763762616 + 2.5 Combine like terms: -0.763762616 + 2.5 = 1.736237384 x = 1.736237384 Simplifying x = 1.736237384

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.263762616, 1.736237384}

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