15x^2-46x+15=0

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Solution for 15x^2-46x+15=0 equation:


Simplifying
15x2 + -46x + 15 = 0

Reorder the terms:
15 + -46x + 15x2 = 0

Solving
15 + -46x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
1 + -3.066666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.066666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3.066666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.066666667x + x2 = 0 + -1
-3.066666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.066666667x + x2 = -1

The x term is -3.066666667x.  Take half its coefficient (-1.533333334).
Square it (2.351111113) and add it to both sides.

Add '2.351111113' to each side of the equation.
-3.066666667x + 2.351111113 + x2 = -1 + 2.351111113

Reorder the terms:
2.351111113 + -3.066666667x + x2 = -1 + 2.351111113

Combine like terms: -1 + 2.351111113 = 1.351111113
2.351111113 + -3.066666667x + x2 = 1.351111113

Factor a perfect square on the left side:
(x + -1.533333334)(x + -1.533333334) = 1.351111113

Calculate the square root of the right side: 1.162373052

Break this problem into two subproblems by setting 
(x + -1.533333334) equal to 1.162373052 and -1.162373052.

Subproblem 1

x + -1.533333334 = 1.162373052 Simplifying x + -1.533333334 = 1.162373052 Reorder the terms: -1.533333334 + x = 1.162373052 Solving -1.533333334 + x = 1.162373052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.533333334' to each side of the equation. -1.533333334 + 1.533333334 + x = 1.162373052 + 1.533333334 Combine like terms: -1.533333334 + 1.533333334 = 0.000000000 0.000000000 + x = 1.162373052 + 1.533333334 x = 1.162373052 + 1.533333334 Combine like terms: 1.162373052 + 1.533333334 = 2.695706386 x = 2.695706386 Simplifying x = 2.695706386

Subproblem 2

x + -1.533333334 = -1.162373052 Simplifying x + -1.533333334 = -1.162373052 Reorder the terms: -1.533333334 + x = -1.162373052 Solving -1.533333334 + x = -1.162373052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.533333334' to each side of the equation. -1.533333334 + 1.533333334 + x = -1.162373052 + 1.533333334 Combine like terms: -1.533333334 + 1.533333334 = 0.000000000 0.000000000 + x = -1.162373052 + 1.533333334 x = -1.162373052 + 1.533333334 Combine like terms: -1.162373052 + 1.533333334 = 0.370960282 x = 0.370960282 Simplifying x = 0.370960282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.695706386, 0.370960282}

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