x(x-10)=12.5

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Solution for x(x-10)=12.5 equation:


Simplifying
x(x + -10) = 12.5

Reorder the terms:
x(-10 + x) = 12.5
(-10 * x + x * x) = 12.5
(-10x + x2) = 12.5

Solving
-10x + x2 = 12.5

Solving for variable 'x'.

Reorder the terms:
-12.5 + -10x + x2 = 12.5 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
-12.5 + -10x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -10x + 12.5 + x2 = 0.0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -10x + x2 = 0.0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -10x + x2 = 0.0 + 12.5
-10x + x2 = 0.0 + 12.5

Combine like terms: 0.0 + 12.5 = 12.5
-10x + x2 = 12.5

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 = 12.5 + 25

Reorder the terms:
25 + -10x + x2 = 12.5 + 25

Combine like terms: 12.5 + 25 = 37.5
25 + -10x + x2 = 37.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 37.5

Calculate the square root of the right side: 6.123724357

Break this problem into two subproblems by setting 
(x + -5) equal to 6.123724357 and -6.123724357.

Subproblem 1

x + -5 = 6.123724357 Simplifying x + -5 = 6.123724357 Reorder the terms: -5 + x = 6.123724357 Solving -5 + x = 6.123724357 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 = 6.123724357 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.123724357 + 5 x = 6.123724357 + 5 Combine like terms: 6.123724357 + 5 = 11.123724357 x = 11.123724357 Simplifying x = 11.123724357

Subproblem 2

x + -5 = -6.123724357 Simplifying x + -5 = -6.123724357 Reorder the terms: -5 + x = -6.123724357 Solving -5 + x = -6.123724357 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 = -6.123724357 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.123724357 + 5 x = -6.123724357 + 5 Combine like terms: -6.123724357 + 5 = -1.123724357 x = -1.123724357 Simplifying x = -1.123724357

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.123724357, -1.123724357}

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