100-x^2-10x=0

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Solution for 100-x^2-10x=0 equation:


Simplifying
100 + -1x2 + -10x = 0

Reorder the terms:
100 + -10x + -1x2 = 0

Solving
100 + -10x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-100 + 10x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 10x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 10x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 10x + x2 = 0 + 100
10x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
10x + x2 = 100

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 100 + 25

Reorder the terms:
25 + 10x + x2 = 100 + 25

Combine like terms: 100 + 25 = 125
25 + 10x + x2 = 125

Factor a perfect square on the left side:
(x + 5)(x + 5) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + 5) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + 5 = 11.180339887 Simplifying x + 5 = 11.180339887 Reorder the terms: 5 + x = 11.180339887 Solving 5 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.180339887 + -5 x = 11.180339887 + -5 Combine like terms: 11.180339887 + -5 = 6.180339887 x = 6.180339887 Simplifying x = 6.180339887

Subproblem 2

x + 5 = -11.180339887 Simplifying x + 5 = -11.180339887 Reorder the terms: 5 + x = -11.180339887 Solving 5 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.180339887 + -5 x = -11.180339887 + -5 Combine like terms: -11.180339887 + -5 = -16.180339887 x = -16.180339887 Simplifying x = -16.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.180339887, -16.180339887}

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