x(x+10)=50

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Solution for x(x+10)=50 equation:


Simplifying
x(x + 10) = 50

Reorder the terms:
x(10 + x) = 50
(10 * x + x * x) = 50
(10x + x2) = 50

Solving
10x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + 10x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 10x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 10x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 10x + x2 = 0 + 50
10x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
10x + x2 = 50

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 = 50 + 25

Reorder the terms:
25 + 10x + x2 = 50 + 25

Combine like terms: 50 + 25 = 75
25 + 10x + x2 = 75

Factor a perfect square on the left side:
(x + 5)(x + 5) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 5) equal to 8.660254038 and -8.660254038.

Subproblem 1

x + 5 = 8.660254038 Simplifying x + 5 = 8.660254038 Reorder the terms: 5 + x = 8.660254038 Solving 5 + x = 8.660254038 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 = 8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.660254038 + -5 x = 8.660254038 + -5 Combine like terms: 8.660254038 + -5 = 3.660254038 x = 3.660254038 Simplifying x = 3.660254038

Subproblem 2

x + 5 = -8.660254038 Simplifying x + 5 = -8.660254038 Reorder the terms: 5 + x = -8.660254038 Solving 5 + x = -8.660254038 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 = -8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.660254038 + -5 x = -8.660254038 + -5 Combine like terms: -8.660254038 + -5 = -13.660254038 x = -13.660254038 Simplifying x = -13.660254038

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.660254038, -13.660254038}

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