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Simplifying 0.2 = 20x + -20x2 Solving 0.2 = 20x + -20x2 Solving for variable 'x'. Reorder the terms: 0.2 + -20x + 20x2 = 20x + -20x + -20x2 + 20x2 Combine like terms: 20x + -20x = 0 0.2 + -20x + 20x2 = 0 + -20x2 + 20x2 0.2 + -20x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 0.2 + -20x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.01 + -1x + x2 = 0 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -1x + -0.01 + x2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + -1x + x2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -1x + x2 = 0 + -0.01 -1x + x2 = 0 + -0.01 Combine like terms: 0 + -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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