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Simplifying -1x2 + 80x + -9 = 0 Reorder the terms: -9 + 80x + -1x2 = 0 Solving -9 + 80x + -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'. 9 + -80x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -80x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -80x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -80x + x2 = 0 + -9 -80x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -80x + x2 = -9 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 = -9 + 1600 Reorder the terms: 1600 + -80x + x2 = -9 + 1600 Combine like terms: -9 + 1600 = 1591 1600 + -80x + x2 = 1591 Factor a perfect square on the left side: (x + -40)(x + -40) = 1591 Calculate the square root of the right side: 39.88734135 Break this problem into two subproblems by setting (x + -40) equal to 39.88734135 and -39.88734135.Subproblem 1
x + -40 = 39.88734135 Simplifying x + -40 = 39.88734135 Reorder the terms: -40 + x = 39.88734135 Solving -40 + x = 39.88734135 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 = 39.88734135 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.88734135 + 40 x = 39.88734135 + 40 Combine like terms: 39.88734135 + 40 = 79.88734135 x = 79.88734135 Simplifying x = 79.88734135Subproblem 2
x + -40 = -39.88734135 Simplifying x + -40 = -39.88734135 Reorder the terms: -40 + x = -39.88734135 Solving -40 + x = -39.88734135 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 = -39.88734135 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.88734135 + 40 x = -39.88734135 + 40 Combine like terms: -39.88734135 + 40 = 0.11265865 x = 0.11265865 Simplifying x = 0.11265865Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.88734135, 0.11265865}
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