x(x+10)=300

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Solution for x(x+10)=300 equation:


Simplifying
x(x + 10) = 300

Reorder the terms:
x(10 + x) = 300
(10 * x + x * x) = 300
(10x + x2) = 300

Solving
10x + x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + 10x + x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 10x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 10x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 10x + x2 = 0 + 300
10x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
10x + x2 = 300

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 = 300 + 25

Reorder the terms:
25 + 10x + x2 = 300 + 25

Combine like terms: 300 + 25 = 325
25 + 10x + x2 = 325

Factor a perfect square on the left side:
(x + 5)(x + 5) = 325

Calculate the square root of the right side: 18.027756377

Break this problem into two subproblems by setting 
(x + 5) equal to 18.027756377 and -18.027756377.

Subproblem 1

x + 5 = 18.027756377 Simplifying x + 5 = 18.027756377 Reorder the terms: 5 + x = 18.027756377 Solving 5 + x = 18.027756377 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 = 18.027756377 + -5 Combine like terms: 5 + -5 = 0 0 + x = 18.027756377 + -5 x = 18.027756377 + -5 Combine like terms: 18.027756377 + -5 = 13.027756377 x = 13.027756377 Simplifying x = 13.027756377

Subproblem 2

x + 5 = -18.027756377 Simplifying x + 5 = -18.027756377 Reorder the terms: 5 + x = -18.027756377 Solving 5 + x = -18.027756377 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 = -18.027756377 + -5 Combine like terms: 5 + -5 = 0 0 + x = -18.027756377 + -5 x = -18.027756377 + -5 Combine like terms: -18.027756377 + -5 = -23.027756377 x = -23.027756377 Simplifying x = -23.027756377

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.027756377, -23.027756377}

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