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Simplifying 0 = -0.01x2 + 0.4x + 6.1 Reorder the terms: 0 = 6.1 + 0.4x + -0.01x2 Solving 0 = 6.1 + 0.4x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -6.1 = -6.1 -6.1 + -0.4x + 0.01x2 = 6.1 + 0.4x + -0.01x2 + -6.1 + -0.4x + 0.01x2 Reorder the terms: -6.1 + -0.4x + 0.01x2 = 6.1 + -6.1 + 0.4x + -0.4x + -0.01x2 + 0.01x2 Combine like terms: 6.1 + -6.1 = 0.0 -6.1 + -0.4x + 0.01x2 = 0.0 + 0.4x + -0.4x + -0.01x2 + 0.01x2 -6.1 + -0.4x + 0.01x2 = 0.4x + -0.4x + -0.01x2 + 0.01x2 Combine like terms: 0.4x + -0.4x = 0.0 -6.1 + -0.4x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -6.1 + -0.4x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -6.1 + -0.4x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -610 + -40x + x2 = 0 Move the constant term to the right: Add '610' to each side of the equation. -610 + -40x + 610 + x2 = 0 + 610 Reorder the terms: -610 + 610 + -40x + x2 = 0 + 610 Combine like terms: -610 + 610 = 0 0 + -40x + x2 = 0 + 610 -40x + x2 = 0 + 610 Combine like terms: 0 + 610 = 610 -40x + x2 = 610 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 = 610 + 400 Reorder the terms: 400 + -40x + x2 = 610 + 400 Combine like terms: 610 + 400 = 1010 400 + -40x + x2 = 1010 Factor a perfect square on the left side: (x + -20)(x + -20) = 1010 Calculate the square root of the right side: 31.780497164 Break this problem into two subproblems by setting (x + -20) equal to 31.780497164 and -31.780497164.Subproblem 1
x + -20 = 31.780497164 Simplifying x + -20 = 31.780497164 Reorder the terms: -20 + x = 31.780497164 Solving -20 + x = 31.780497164 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 = 31.780497164 + 20 Combine like terms: -20 + 20 = 0 0 + x = 31.780497164 + 20 x = 31.780497164 + 20 Combine like terms: 31.780497164 + 20 = 51.780497164 x = 51.780497164 Simplifying x = 51.780497164Subproblem 2
x + -20 = -31.780497164 Simplifying x + -20 = -31.780497164 Reorder the terms: -20 + x = -31.780497164 Solving -20 + x = -31.780497164 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 = -31.780497164 + 20 Combine like terms: -20 + 20 = 0 0 + x = -31.780497164 + 20 x = -31.780497164 + 20 Combine like terms: -31.780497164 + 20 = -11.780497164 x = -11.780497164 Simplifying x = -11.780497164Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.780497164, -11.780497164}
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