(x*x)+(20*x)=400

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Solution for (x*x)+(20*x)=400 equation:


Simplifying
(x * x) + (20x) = 400

Multiply x * x
(x2) + (20x) = 400
x2 + (20x) = 400

Reorder the terms:
(20x) + x2 = 400

Solving
(20x) + x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + (20x) + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + (20x) + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + (20x) + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + (20x) + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + (20x) + x2 = 0 + 400
(20x) + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
(20x) + x2 = 400

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 = 400 + 100

Reorder the terms:
100 + (20x) + x2 = 400 + 100

Combine like terms: 400 + 100 = 500
100 + (20x) + x2 = 500

Factor a perfect square on the left side:
(x + 10)(x + 10) = 500

Calculate the square root of the right side: 22.360679775

Break this problem into two subproblems by setting 
(x + 10) equal to 22.360679775 and -22.360679775.

Subproblem 1

x + 10 = 22.360679775 Simplifying x + 10 = 22.360679775 Reorder the terms: 10 + x = 22.360679775 Solving 10 + x = 22.360679775 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 = 22.360679775 + -10 Combine like terms: 10 + -10 = 0 0 + x = 22.360679775 + -10 x = 22.360679775 + -10 Combine like terms: 22.360679775 + -10 = 12.360679775 x = 12.360679775 Simplifying x = 12.360679775

Subproblem 2

x + 10 = -22.360679775 Simplifying x + 10 = -22.360679775 Reorder the terms: 10 + x = -22.360679775 Solving 10 + x = -22.360679775 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 = -22.360679775 + -10 Combine like terms: 10 + -10 = 0 0 + x = -22.360679775 + -10 x = -22.360679775 + -10 Combine like terms: -22.360679775 + -10 = -32.360679775 x = -32.360679775 Simplifying x = -32.360679775

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.360679775, -32.360679775}

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