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Simplifying -1x2 + 40x + -80 = 0 Reorder the terms: -80 + 40x + -1x2 = 0 Solving -80 + 40x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 80 + -40x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -40x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -40x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -40x + x2 = 0 + -80 -40x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -40x + x2 = -80 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 = -80 + 400 Reorder the terms: 400 + -40x + x2 = -80 + 400 Combine like terms: -80 + 400 = 320 400 + -40x + x2 = 320 Factor a perfect square on the left side: (x + -20)(x + -20) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + -20) equal to 17.88854382 and -17.88854382.Subproblem 1
x + -20 = 17.88854382 Simplifying x + -20 = 17.88854382 Reorder the terms: -20 + x = 17.88854382 Solving -20 + x = 17.88854382 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 = 17.88854382 + 20 Combine like terms: -20 + 20 = 0 0 + x = 17.88854382 + 20 x = 17.88854382 + 20 Combine like terms: 17.88854382 + 20 = 37.88854382 x = 37.88854382 Simplifying x = 37.88854382Subproblem 2
x + -20 = -17.88854382 Simplifying x + -20 = -17.88854382 Reorder the terms: -20 + x = -17.88854382 Solving -20 + x = -17.88854382 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 = -17.88854382 + 20 Combine like terms: -20 + 20 = 0 0 + x = -17.88854382 + 20 x = -17.88854382 + 20 Combine like terms: -17.88854382 + 20 = 2.11145618 x = 2.11145618 Simplifying x = 2.11145618Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.88854382, 2.11145618}
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