(10+x)(10+x)=200

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Solution for (10+x)(10+x)=200 equation:


Simplifying
(10 + x)(10 + x) = 200

Multiply (10 + x) * (10 + x)
(10(10 + x) + x(10 + x)) = 200
((10 * 10 + x * 10) + x(10 + x)) = 200
((100 + 10x) + x(10 + x)) = 200
(100 + 10x + (10 * x + x * x)) = 200
(100 + 10x + (10x + x2)) = 200

Combine like terms: 10x + 10x = 20x
(100 + 20x + x2) = 200

Solving
100 + 20x + x2 = 200

Solving for variable 'x'.

Reorder the terms:
100 + -200 + 20x + x2 = 200 + -200

Combine like terms: 100 + -200 = -100
-100 + 20x + x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-100 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 20x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 20x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 20x + x2 = 0 + 100
20x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
20x + x2 = 100

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 100 + 100

Reorder the terms:
100 + 20x + x2 = 100 + 100

Combine like terms: 100 + 100 = 200
100 + 20x + x2 = 200

Factor a perfect square on the left side:
(x + 10)(x + 10) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(x + 10) equal to 14.142135624 and -14.142135624.

Subproblem 1

x + 10 = 14.142135624 Simplifying x + 10 = 14.142135624 Reorder the terms: 10 + x = 14.142135624 Solving 10 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.142135624 + -10 x = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 x = 4.142135624 Simplifying x = 4.142135624

Subproblem 2

x + 10 = -14.142135624 Simplifying x + 10 = -14.142135624 Reorder the terms: 10 + x = -14.142135624 Solving 10 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.142135624 + -10 x = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 x = -24.142135624 Simplifying x = -24.142135624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.142135624, -24.142135624}

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