15x^2-100x+74=0

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Solution for 15x^2-100x+74=0 equation: 


Simplifying
15x2 + -100x + 74 = 0

Reorder the terms:
74 + -100x + 15x2 = 0

Solving
74 + -100x + 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'.
4.933333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-4.933333333' to each side of the equation.
4.933333333 + -6.666666667x + -4.933333333 + x2 = 0 + -4.933333333

Reorder the terms:
4.933333333 + -4.933333333 + -6.666666667x + x2 = 0 + -4.933333333

Combine like terms: 4.933333333 + -4.933333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -4.933333333
-6.666666667x + x2 = 0 + -4.933333333

Combine like terms: 0 + -4.933333333 = -4.933333333
-6.666666667x + x2 = -4.933333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -4.933333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -4.933333333 + 11.11111112

Combine like terms: -4.933333333 + 11.11111112 = 6.177777787
11.11111112 + -6.666666667x + x2 = 6.177777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 6.177777787

Calculate the square root of the right side: 2.485513586

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.485513586 and -2.485513586.


Subproblem 1
x + -3.333333334 = 2.485513586

Simplifying
x + -3.333333334 = 2.485513586

Reorder the terms:
-3.333333334 + x = 2.485513586

Solving
-3.333333334 + x = 2.485513586

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.485513586 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.485513586 + 3.333333334
x = 2.485513586 + 3.333333334

Combine like terms: 2.485513586 + 3.333333334 = 5.81884692
x = 5.81884692

Simplifying
x = 5.81884692


Subproblem 2
x + -3.333333334 = -2.485513586

Simplifying
x + -3.333333334 = -2.485513586

Reorder the terms:
-3.333333334 + x = -2.485513586

Solving
-3.333333334 + x = -2.485513586

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.485513586 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.485513586 + 3.333333334
x = -2.485513586 + 3.333333334

Combine like terms: -2.485513586 + 3.333333334 = 0.847819748
x = 0.847819748

Simplifying
x = 0.847819748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.81884692, 0.847819748}

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