15x+13x(14-x)=198

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Solution for 15x+13x(14-x)=198 equation:


Simplifying
15x + 13x(14 + -1x) = 198
15x + (14 * 13x + -1x * 13x) = 198
15x + (182x + -13x2) = 198

Combine like terms: 15x + 182x = 197x
197x + -13x2 = 198

Solving
197x + -13x2 = 198

Solving for variable 'x'.

Reorder the terms:
-198 + 197x + -13x2 = 198 + -198

Combine like terms: 198 + -198 = 0
-198 + 197x + -13x2 = 0

Begin completing the square.  Divide all terms by
-13 the coefficient of the squared term: 

Divide each side by '-13'.
15.23076923 + -15.15384615x + x2 = 0

Move the constant term to the right:

Add '-15.23076923' to each side of the equation.
15.23076923 + -15.15384615x + -15.23076923 + x2 = 0 + -15.23076923

Reorder the terms:
15.23076923 + -15.23076923 + -15.15384615x + x2 = 0 + -15.23076923

Combine like terms: 15.23076923 + -15.23076923 = 0.00000000
0.00000000 + -15.15384615x + x2 = 0 + -15.23076923
-15.15384615x + x2 = 0 + -15.23076923

Combine like terms: 0 + -15.23076923 = -15.23076923
-15.15384615x + x2 = -15.23076923

The x term is -15.15384615x.  Take half its coefficient (-7.576923075).
Square it (57.40976328) and add it to both sides.

Add '57.40976328' to each side of the equation.
-15.15384615x + 57.40976328 + x2 = -15.23076923 + 57.40976328

Reorder the terms:
57.40976328 + -15.15384615x + x2 = -15.23076923 + 57.40976328

Combine like terms: -15.23076923 + 57.40976328 = 42.17899405
57.40976328 + -15.15384615x + x2 = 42.17899405

Factor a perfect square on the left side:
(x + -7.576923075)(x + -7.576923075) = 42.17899405

Calculate the square root of the right side: 6.494535707

Break this problem into two subproblems by setting 
(x + -7.576923075) equal to 6.494535707 and -6.494535707.

Subproblem 1

x + -7.576923075 = 6.494535707 Simplifying x + -7.576923075 = 6.494535707 Reorder the terms: -7.576923075 + x = 6.494535707 Solving -7.576923075 + x = 6.494535707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.576923075' to each side of the equation. -7.576923075 + 7.576923075 + x = 6.494535707 + 7.576923075 Combine like terms: -7.576923075 + 7.576923075 = 0.000000000 0.000000000 + x = 6.494535707 + 7.576923075 x = 6.494535707 + 7.576923075 Combine like terms: 6.494535707 + 7.576923075 = 14.071458782 x = 14.071458782 Simplifying x = 14.071458782

Subproblem 2

x + -7.576923075 = -6.494535707 Simplifying x + -7.576923075 = -6.494535707 Reorder the terms: -7.576923075 + x = -6.494535707 Solving -7.576923075 + x = -6.494535707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.576923075' to each side of the equation. -7.576923075 + 7.576923075 + x = -6.494535707 + 7.576923075 Combine like terms: -7.576923075 + 7.576923075 = 0.000000000 0.000000000 + x = -6.494535707 + 7.576923075 x = -6.494535707 + 7.576923075 Combine like terms: -6.494535707 + 7.576923075 = 1.082387368 x = 1.082387368 Simplifying x = 1.082387368

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.071458782, 1.082387368}

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