x(x-3)=100

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Solution for x(x-3)=100 equation:


Simplifying
x(x + -3) = 100

Reorder the terms:
x(-3 + x) = 100
(-3 * x + x * x) = 100
(-3x + x2) = 100

Solving
-3x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -3x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -3x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -3x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -3x + x2 = 0 + 100
-3x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-3x + x2 = 100

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 100 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 100 + 2.25

Combine like terms: 100 + 2.25 = 102.25
2.25 + -3x + x2 = 102.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + -1.5) equal to 10.111874208 and -10.111874208.

Subproblem 1

x + -1.5 = 10.111874208 Simplifying x + -1.5 = 10.111874208 Reorder the terms: -1.5 + x = 10.111874208 Solving -1.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 10.111874208 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.111874208 + 1.5 x = 10.111874208 + 1.5 Combine like terms: 10.111874208 + 1.5 = 11.611874208 x = 11.611874208 Simplifying x = 11.611874208

Subproblem 2

x + -1.5 = -10.111874208 Simplifying x + -1.5 = -10.111874208 Reorder the terms: -1.5 + x = -10.111874208 Solving -1.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -10.111874208 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.111874208 + 1.5 x = -10.111874208 + 1.5 Combine like terms: -10.111874208 + 1.5 = -8.611874208 x = -8.611874208 Simplifying x = -8.611874208

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.611874208, -8.611874208}

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