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Simplifying X(X + -2) = 20 Reorder the terms: X(-2 + X) = 20 (-2 * X + X * X) = 20 (-2X + X2) = 20 Solving -2X + X2 = 20 Solving for variable 'X'. Reorder the terms: -20 + -2X + X2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -2X + 20 + X2 = 0 + 20 Reorder the terms: -20 + 20 + -2X + X2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2X + X2 = 0 + 20 -2X + X2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2X + X2 = 20 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 20 + 1 Reorder the terms: 1 + -2X + X2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2X + X2 = 21 Factor a perfect square on the left side: (X + -1)(X + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (X + -1) equal to 4.582575695 and -4.582575695.Subproblem 1
X + -1 = 4.582575695 Simplifying X + -1 = 4.582575695 Reorder the terms: -1 + X = 4.582575695 Solving -1 + X = 4.582575695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + X = 4.582575695 + 1 X = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 X = 5.582575695 Simplifying X = 5.582575695Subproblem 2
X + -1 = -4.582575695 Simplifying X + -1 = -4.582575695 Reorder the terms: -1 + X = -4.582575695 Solving -1 + X = -4.582575695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + X = -4.582575695 + 1 X = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 X = -3.582575695 Simplifying X = -3.582575695Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.582575695, -3.582575695}
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