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Simplifying 40x + -1x2 = 99.584 Solving 40x + -1x2 = 99.584 Solving for variable 'x'. Reorder the terms: -99.584 + 40x + -1x2 = 99.584 + -99.584 Combine like terms: 99.584 + -99.584 = 0.000 -99.584 + 40x + -1x2 = 0.000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 99.584 + -40x + x2 = 0.000 Move the constant term to the right: Add '-99.584' to each side of the equation. 99.584 + -40x + -99.584 + x2 = 0.000 + -99.584 Reorder the terms: 99.584 + -99.584 + -40x + x2 = 0.000 + -99.584 Combine like terms: 99.584 + -99.584 = 0.000 0.000 + -40x + x2 = 0.000 + -99.584 -40x + x2 = 0.000 + -99.584 Combine like terms: 0.000 + -99.584 = -99.584 -40x + x2 = -99.584 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 = -99.584 + 400 Reorder the terms: 400 + -40x + x2 = -99.584 + 400 Combine like terms: -99.584 + 400 = 300.416 400 + -40x + x2 = 300.416 Factor a perfect square on the left side: (x + -20)(x + -20) = 300.416 Calculate the square root of the right side: 17.332512801 Break this problem into two subproblems by setting (x + -20) equal to 17.332512801 and -17.332512801.Subproblem 1
x + -20 = 17.332512801 Simplifying x + -20 = 17.332512801 Reorder the terms: -20 + x = 17.332512801 Solving -20 + x = 17.332512801 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 = 17.332512801 + 20 Combine like terms: -20 + 20 = 0 0 + x = 17.332512801 + 20 x = 17.332512801 + 20 Combine like terms: 17.332512801 + 20 = 37.332512801 x = 37.332512801 Simplifying x = 37.332512801Subproblem 2
x + -20 = -17.332512801 Simplifying x + -20 = -17.332512801 Reorder the terms: -20 + x = -17.332512801 Solving -20 + x = -17.332512801 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 = -17.332512801 + 20 Combine like terms: -20 + 20 = 0 0 + x = -17.332512801 + 20 x = -17.332512801 + 20 Combine like terms: -17.332512801 + 20 = 2.667487199 x = 2.667487199 Simplifying x = 2.667487199Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.332512801, 2.667487199}
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