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Simplifying x2 + -40x + 388 = 0 Reorder the terms: 388 + -40x + x2 = 0 Solving 388 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-388' to each side of the equation. 388 + -40x + -388 + x2 = 0 + -388 Reorder the terms: 388 + -388 + -40x + x2 = 0 + -388 Combine like terms: 388 + -388 = 0 0 + -40x + x2 = 0 + -388 -40x + x2 = 0 + -388 Combine like terms: 0 + -388 = -388 -40x + x2 = -388 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -388 + 400 Reorder the terms: 400 + -40x + x2 = -388 + 400 Combine like terms: -388 + 400 = 12 400 + -40x + x2 = 12 Factor a perfect square on the left side: (x + -20)(x + -20) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -20) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -20 = 3.464101615 Simplifying x + -20 = 3.464101615 Reorder the terms: -20 + x = 3.464101615 Solving -20 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 3.464101615 + 20 Combine like terms: -20 + 20 = 0 0 + x = 3.464101615 + 20 x = 3.464101615 + 20 Combine like terms: 3.464101615 + 20 = 23.464101615 x = 23.464101615 Simplifying x = 23.464101615Subproblem 2
x + -20 = -3.464101615 Simplifying x + -20 = -3.464101615 Reorder the terms: -20 + x = -3.464101615 Solving -20 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -3.464101615 + 20 Combine like terms: -20 + 20 = 0 0 + x = -3.464101615 + 20 x = -3.464101615 + 20 Combine like terms: -3.464101615 + 20 = 16.535898385 x = 16.535898385 Simplifying x = 16.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.464101615, 16.535898385}
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