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