(253-x)(2x-x)=0.17

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Solution for (253-x)(2x-x)=0.17 equation:


Simplifying
(253 + -1x)(2x + -1x) = 0.17

Combine like terms: 2x + -1x = 1x
(253 + -1x)(1x) = 0.17

Remove parenthesis around (1x)
(253 + -1x) * 1x = 0.17

Reorder the terms for easier multiplication:
1x(253 + -1x) = 0.17
(253 * 1x + -1x * 1x) = 0.17
(253x + -1x2) = 0.17

Solving
253x + -1x2 = 0.17

Solving for variable 'x'.

Reorder the terms:
-0.17 + 253x + -1x2 = 0.17 + -0.17

Combine like terms: 0.17 + -0.17 = 0.00
-0.17 + 253x + -1x2 = 0.00

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.17 + -253x + x2 = 0.00

Move the constant term to the right:

Add '-0.17' to each side of the equation.
0.17 + -253x + -0.17 + x2 = 0.00 + -0.17

Reorder the terms:
0.17 + -0.17 + -253x + x2 = 0.00 + -0.17

Combine like terms: 0.17 + -0.17 = 0.00
0.00 + -253x + x2 = 0.00 + -0.17
-253x + x2 = 0.00 + -0.17

Combine like terms: 0.00 + -0.17 = -0.17
-253x + x2 = -0.17

The x term is -253x.  Take half its coefficient (-126.5).
Square it (16002.25) and add it to both sides.

Add '16002.25' to each side of the equation.
-253x + 16002.25 + x2 = -0.17 + 16002.25

Reorder the terms:
16002.25 + -253x + x2 = -0.17 + 16002.25

Combine like terms: -0.17 + 16002.25 = 16002.08
16002.25 + -253x + x2 = 16002.08

Factor a perfect square on the left side:
(x + -126.5)(x + -126.5) = 16002.08

Calculate the square root of the right side: 126.499328061

Break this problem into two subproblems by setting 
(x + -126.5) equal to 126.499328061 and -126.499328061.

Subproblem 1

x + -126.5 = 126.499328061 Simplifying x + -126.5 = 126.499328061 Reorder the terms: -126.5 + x = 126.499328061 Solving -126.5 + x = 126.499328061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '126.5' to each side of the equation. -126.5 + 126.5 + x = 126.499328061 + 126.5 Combine like terms: -126.5 + 126.5 = 0.0 0.0 + x = 126.499328061 + 126.5 x = 126.499328061 + 126.5 Combine like terms: 126.499328061 + 126.5 = 252.999328061 x = 252.999328061 Simplifying x = 252.999328061

Subproblem 2

x + -126.5 = -126.499328061 Simplifying x + -126.5 = -126.499328061 Reorder the terms: -126.5 + x = -126.499328061 Solving -126.5 + x = -126.499328061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '126.5' to each side of the equation. -126.5 + 126.5 + x = -126.499328061 + 126.5 Combine like terms: -126.5 + 126.5 = 0.0 0.0 + x = -126.499328061 + 126.5 x = -126.499328061 + 126.5 Combine like terms: -126.499328061 + 126.5 = 0.000671939 x = 0.000671939 Simplifying x = 0.000671939

Solution

The solution to the problem is based on the solutions from the subproblems. x = {252.999328061, 0.000671939}

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