0=x^2-10x-900

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Solution for 0=x^2-10x-900 equation:


Simplifying
0 = x2 + -10x + -900

Reorder the terms:
0 = -900 + -10x + x2

Solving
0 = -900 + -10x + x2

Solving for variable 'x'.

Combine like terms: 0 + 900 = 900
900 + 10x + -1x2 = -900 + -10x + x2 + 900 + 10x + -1x2

Reorder the terms:
900 + 10x + -1x2 = -900 + 900 + -10x + 10x + x2 + -1x2

Combine like terms: -900 + 900 = 0
900 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2
900 + 10x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
900 + 10x + -1x2 = 0 + x2 + -1x2
900 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
900 + 10x + -1x2 = 0

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

Divide each side by '-1'.
-900 + -10x + x2 = 0

Move the constant term to the right:

Add '900' to each side of the equation.
-900 + -10x + 900 + x2 = 0 + 900

Reorder the terms:
-900 + 900 + -10x + x2 = 0 + 900

Combine like terms: -900 + 900 = 0
0 + -10x + x2 = 0 + 900
-10x + x2 = 0 + 900

Combine like terms: 0 + 900 = 900
-10x + x2 = 900

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 = 900 + 25

Reorder the terms:
25 + -10x + x2 = 900 + 25

Combine like terms: 900 + 25 = 925
25 + -10x + x2 = 925

Factor a perfect square on the left side:
(x + -5)(x + -5) = 925

Calculate the square root of the right side: 30.413812651

Break this problem into two subproblems by setting 
(x + -5) equal to 30.413812651 and -30.413812651.

Subproblem 1

x + -5 = 30.413812651 Simplifying x + -5 = 30.413812651 Reorder the terms: -5 + x = 30.413812651 Solving -5 + x = 30.413812651 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 = 30.413812651 + 5 Combine like terms: -5 + 5 = 0 0 + x = 30.413812651 + 5 x = 30.413812651 + 5 Combine like terms: 30.413812651 + 5 = 35.413812651 x = 35.413812651 Simplifying x = 35.413812651

Subproblem 2

x + -5 = -30.413812651 Simplifying x + -5 = -30.413812651 Reorder the terms: -5 + x = -30.413812651 Solving -5 + x = -30.413812651 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 = -30.413812651 + 5 Combine like terms: -5 + 5 = 0 0 + x = -30.413812651 + 5 x = -30.413812651 + 5 Combine like terms: -30.413812651 + 5 = -25.413812651 x = -25.413812651 Simplifying x = -25.413812651

Solution

The solution to the problem is based on the solutions from the subproblems. x = {35.413812651, -25.413812651}

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