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Simplifying 0.25x2 + -20x = 15 Reorder the terms: -20x + 0.25x2 = 15 Solving -20x + 0.25x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -20x + 0.25x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -20x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -60 + -80x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -80x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -80x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -80x + x2 = 0 + 60 -80x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -80x + x2 = 60 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 60 + 1600 Reorder the terms: 1600 + -80x + x2 = 60 + 1600 Combine like terms: 60 + 1600 = 1660 1600 + -80x + x2 = 1660 Factor a perfect square on the left side: (x + -40)(x + -40) = 1660 Calculate the square root of the right side: 40.743097575 Break this problem into two subproblems by setting (x + -40) equal to 40.743097575 and -40.743097575.Subproblem 1
x + -40 = 40.743097575 Simplifying x + -40 = 40.743097575 Reorder the terms: -40 + x = 40.743097575 Solving -40 + x = 40.743097575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 40.743097575 + 40 Combine like terms: -40 + 40 = 0 0 + x = 40.743097575 + 40 x = 40.743097575 + 40 Combine like terms: 40.743097575 + 40 = 80.743097575 x = 80.743097575 Simplifying x = 80.743097575Subproblem 2
x + -40 = -40.743097575 Simplifying x + -40 = -40.743097575 Reorder the terms: -40 + x = -40.743097575 Solving -40 + x = -40.743097575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -40.743097575 + 40 Combine like terms: -40 + 40 = 0 0 + x = -40.743097575 + 40 x = -40.743097575 + 40 Combine like terms: -40.743097575 + 40 = -0.743097575 x = -0.743097575 Simplifying x = -0.743097575Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.743097575, -0.743097575}
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