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Simplifying 2(1 + -1X)(X) = 0.02 Reorder the terms for easier multiplication: 2X(1 + -1X) = 0.02 (1 * 2X + -1X * 2X) = 0.02 (2X + -2X2) = 0.02 Solving 2X + -2X2 = 0.02 Solving for variable 'X'. Reorder the terms: -0.02 + 2X + -2X2 = 0.02 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 -0.02 + 2X + -2X2 = 0.00 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.01 + -1X + X2 = 0.00 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -1X + -0.01 + X2 = 0.00 + -0.01 Reorder the terms: 0.01 + -0.01 + -1X + X2 = 0.00 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -1X + X2 = 0.00 + -0.01 -1X + X2 = 0.00 + -0.01 Combine like terms: 0.00 + -0.01 = -0.01 -1X + X2 = -0.01 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = -0.01 + 0.25 Reorder the terms: 0.25 + -1X + X2 = -0.01 + 0.25 Combine like terms: -0.01 + 0.25 = 0.24 0.25 + -1X + X2 = 0.24 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (X + -0.5) equal to 0.489897949 and -0.489897949.Subproblem 1
X + -0.5 = 0.489897949 Simplifying X + -0.5 = 0.489897949 Reorder the terms: -0.5 + X = 0.489897949 Solving -0.5 + X = 0.489897949 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 0.489897949 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 0.489897949 + 0.5 X = 0.489897949 + 0.5 Combine like terms: 0.489897949 + 0.5 = 0.989897949 X = 0.989897949 Simplifying X = 0.989897949Subproblem 2
X + -0.5 = -0.489897949 Simplifying X + -0.5 = -0.489897949 Reorder the terms: -0.5 + X = -0.489897949 Solving -0.5 + X = -0.489897949 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -0.489897949 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -0.489897949 + 0.5 X = -0.489897949 + 0.5 Combine like terms: -0.489897949 + 0.5 = 0.010102051 X = 0.010102051 Simplifying X = 0.010102051Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.989897949, 0.010102051}
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