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Simplifying 20x + -20x2 = 3.4 Solving 20x + -20x2 = 3.4 Solving for variable 'x'. Reorder the terms: -3.4 + 20x + -20x2 = 3.4 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 -3.4 + 20x + -20x2 = 0.0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. 0.17 + -1x + x2 = 0.0 Move the constant term to the right: Add '-0.17' to each side of the equation. 0.17 + -1x + -0.17 + x2 = 0.0 + -0.17 Reorder the terms: 0.17 + -0.17 + -1x + x2 = 0.0 + -0.17 Combine like terms: 0.17 + -0.17 = 0.00 0.00 + -1x + x2 = 0.0 + -0.17 -1x + x2 = 0.0 + -0.17 Combine like terms: 0.0 + -0.17 = -0.17 -1x + x2 = -0.17 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 = -0.17 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.17 + 0.25 Combine like terms: -0.17 + 0.25 = 0.08 0.25 + -1x + x2 = 0.08 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting (x + -0.5) equal to 0.282842712 and -0.282842712.Subproblem 1
x + -0.5 = 0.282842712 Simplifying x + -0.5 = 0.282842712 Reorder the terms: -0.5 + x = 0.282842712 Solving -0.5 + x = 0.282842712 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 = 0.282842712 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.282842712 + 0.5 x = 0.282842712 + 0.5 Combine like terms: 0.282842712 + 0.5 = 0.782842712 x = 0.782842712 Simplifying x = 0.782842712Subproblem 2
x + -0.5 = -0.282842712 Simplifying x + -0.5 = -0.282842712 Reorder the terms: -0.5 + x = -0.282842712 Solving -0.5 + x = -0.282842712 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 = -0.282842712 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.282842712 + 0.5 x = -0.282842712 + 0.5 Combine like terms: -0.282842712 + 0.5 = 0.217157288 x = 0.217157288 Simplifying x = 0.217157288Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.782842712, 0.217157288}
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