x(x+25)=10

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Solution for x(x+25)=10 equation:


Simplifying
x(x + 25) = 10

Reorder the terms:
x(25 + x) = 10
(25 * x + x * x) = 10
(25x + x2) = 10

Solving
25x + x2 = 10

Solving for variable 'x'.

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

Combine like terms: 10 + -10 = 0
-10 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 25x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 25x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 25x + x2 = 0 + 10
25x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
25x + x2 = 10

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 10 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 10 + 156.25

Combine like terms: 10 + 156.25 = 166.25
156.25 + 25x + x2 = 166.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 166.25

Calculate the square root of the right side: 12.893796958

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.893796958 and -12.893796958.

Subproblem 1

x + 12.5 = 12.893796958 Simplifying x + 12.5 = 12.893796958 Reorder the terms: 12.5 + x = 12.893796958 Solving 12.5 + x = 12.893796958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.893796958 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.893796958 + -12.5 x = 12.893796958 + -12.5 Combine like terms: 12.893796958 + -12.5 = 0.393796958 x = 0.393796958 Simplifying x = 0.393796958

Subproblem 2

x + 12.5 = -12.893796958 Simplifying x + 12.5 = -12.893796958 Reorder the terms: 12.5 + x = -12.893796958 Solving 12.5 + x = -12.893796958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.893796958 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.893796958 + -12.5 x = -12.893796958 + -12.5 Combine like terms: -12.893796958 + -12.5 = -25.393796958 x = -25.393796958 Simplifying x = -25.393796958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.393796958, -25.393796958}

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