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Simplifying 0 = x2 + -40x + 360 Reorder the terms: 0 = 360 + -40x + x2 Solving 0 = 360 + -40x + x2 Solving for variable 'x'. Combine like terms: 0 + -360 = -360 -360 + 40x + -1x2 = 360 + -40x + x2 + -360 + 40x + -1x2 Reorder the terms: -360 + 40x + -1x2 = 360 + -360 + -40x + 40x + x2 + -1x2 Combine like terms: 360 + -360 = 0 -360 + 40x + -1x2 = 0 + -40x + 40x + x2 + -1x2 -360 + 40x + -1x2 = -40x + 40x + x2 + -1x2 Combine like terms: -40x + 40x = 0 -360 + 40x + -1x2 = 0 + x2 + -1x2 -360 + 40x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -360 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 360 + -40x + x2 = 0 Move the constant term to the right: Add '-360' to each side of the equation. 360 + -40x + -360 + x2 = 0 + -360 Reorder the terms: 360 + -360 + -40x + x2 = 0 + -360 Combine like terms: 360 + -360 = 0 0 + -40x + x2 = 0 + -360 -40x + x2 = 0 + -360 Combine like terms: 0 + -360 = -360 -40x + x2 = -360 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 = -360 + 400 Reorder the terms: 400 + -40x + x2 = -360 + 400 Combine like terms: -360 + 400 = 40 400 + -40x + x2 = 40 Factor a perfect square on the left side: (x + -20)(x + -20) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -20) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -20 = 6.32455532 Simplifying x + -20 = 6.32455532 Reorder the terms: -20 + x = 6.32455532 Solving -20 + x = 6.32455532 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 = 6.32455532 + 20 Combine like terms: -20 + 20 = 0 0 + x = 6.32455532 + 20 x = 6.32455532 + 20 Combine like terms: 6.32455532 + 20 = 26.32455532 x = 26.32455532 Simplifying x = 26.32455532Subproblem 2
x + -20 = -6.32455532 Simplifying x + -20 = -6.32455532 Reorder the terms: -20 + x = -6.32455532 Solving -20 + x = -6.32455532 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 = -6.32455532 + 20 Combine like terms: -20 + 20 = 0 0 + x = -6.32455532 + 20 x = -6.32455532 + 20 Combine like terms: -6.32455532 + 20 = 13.67544468 x = 13.67544468 Simplifying x = 13.67544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.32455532, 13.67544468}
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