0=x^2-100x+160

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Solution for 0=x^2-100x+160 equation:


Simplifying
0 = x2 + -100x + 160

Reorder the terms:
0 = 160 + -100x + x2

Solving
0 = 160 + -100x + x2

Solving for variable 'x'.

Combine like terms: 0 + -160 = -160
-160 + 100x + -1x2 = 160 + -100x + x2 + -160 + 100x + -1x2

Reorder the terms:
-160 + 100x + -1x2 = 160 + -160 + -100x + 100x + x2 + -1x2

Combine like terms: 160 + -160 = 0
-160 + 100x + -1x2 = 0 + -100x + 100x + x2 + -1x2
-160 + 100x + -1x2 = -100x + 100x + x2 + -1x2

Combine like terms: -100x + 100x = 0
-160 + 100x + -1x2 = 0 + x2 + -1x2
-160 + 100x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-160 + 100x + -1x2 = 0

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

Divide each side by '-1'.
160 + -100x + x2 = 0

Move the constant term to the right:

Add '-160' to each side of the equation.
160 + -100x + -160 + x2 = 0 + -160

Reorder the terms:
160 + -160 + -100x + x2 = 0 + -160

Combine like terms: 160 + -160 = 0
0 + -100x + x2 = 0 + -160
-100x + x2 = 0 + -160

Combine like terms: 0 + -160 = -160
-100x + x2 = -160

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -160 + 2500

Reorder the terms:
2500 + -100x + x2 = -160 + 2500

Combine like terms: -160 + 2500 = 2340
2500 + -100x + x2 = 2340

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2340

Calculate the square root of the right side: 48.37354649

Break this problem into two subproblems by setting 
(x + -50) equal to 48.37354649 and -48.37354649.

Subproblem 1

x + -50 = 48.37354649 Simplifying x + -50 = 48.37354649 Reorder the terms: -50 + x = 48.37354649 Solving -50 + x = 48.37354649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 48.37354649 + 50 Combine like terms: -50 + 50 = 0 0 + x = 48.37354649 + 50 x = 48.37354649 + 50 Combine like terms: 48.37354649 + 50 = 98.37354649 x = 98.37354649 Simplifying x = 98.37354649

Subproblem 2

x + -50 = -48.37354649 Simplifying x + -50 = -48.37354649 Reorder the terms: -50 + x = -48.37354649 Solving -50 + x = -48.37354649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -48.37354649 + 50 Combine like terms: -50 + 50 = 0 0 + x = -48.37354649 + 50 x = -48.37354649 + 50 Combine like terms: -48.37354649 + 50 = 1.62645351 x = 1.62645351 Simplifying x = 1.62645351

Solution

The solution to the problem is based on the solutions from the subproblems. x = {98.37354649, 1.62645351}

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