9x^2-25x+15=0

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Solution for 9x^2-25x+15=0 equation:


Simplifying
9x2 + -25x + 15 = 0

Reorder the terms:
15 + -25x + 9x2 = 0

Solving
15 + -25x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
1.666666667 + -2.777777778x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -2.777777778x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -2.777777778x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -2.777777778x + x2 = 0 + -1.666666667
-2.777777778x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-2.777777778x + x2 = -1.666666667

The x term is -2.777777778x.  Take half its coefficient (-1.388888889).
Square it (1.929012346) and add it to both sides.

Add '1.929012346' to each side of the equation.
-2.777777778x + 1.929012346 + x2 = -1.666666667 + 1.929012346

Reorder the terms:
1.929012346 + -2.777777778x + x2 = -1.666666667 + 1.929012346

Combine like terms: -1.666666667 + 1.929012346 = 0.262345679
1.929012346 + -2.777777778x + x2 = 0.262345679

Factor a perfect square on the left side:
(x + -1.388888889)(x + -1.388888889) = 0.262345679

Calculate the square root of the right side: 0.512196914

Break this problem into two subproblems by setting 
(x + -1.388888889) equal to 0.512196914 and -0.512196914.

Subproblem 1

x + -1.388888889 = 0.512196914 Simplifying x + -1.388888889 = 0.512196914 Reorder the terms: -1.388888889 + x = 0.512196914 Solving -1.388888889 + x = 0.512196914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = 0.512196914 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 0.512196914 + 1.388888889 x = 0.512196914 + 1.388888889 Combine like terms: 0.512196914 + 1.388888889 = 1.901085803 x = 1.901085803 Simplifying x = 1.901085803

Subproblem 2

x + -1.388888889 = -0.512196914 Simplifying x + -1.388888889 = -0.512196914 Reorder the terms: -1.388888889 + x = -0.512196914 Solving -1.388888889 + x = -0.512196914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = -0.512196914 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -0.512196914 + 1.388888889 x = -0.512196914 + 1.388888889 Combine like terms: -0.512196914 + 1.388888889 = 0.876691975 x = 0.876691975 Simplifying x = 0.876691975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.901085803, 0.876691975}

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