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Simplifying -0.6x2 + 259.2x = 216 Reorder the terms: 259.2x + -0.6x2 = 216 Solving 259.2x + -0.6x2 = 216 Solving for variable 'x'. Reorder the terms: -216 + 259.2x + -0.6x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + 259.2x + -0.6x2 = 0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 360 + -432x + x2 = 0 Move the constant term to the right: Add '-360' to each side of the equation. 360 + -432x + -360 + x2 = 0 + -360 Reorder the terms: 360 + -360 + -432x + x2 = 0 + -360 Combine like terms: 360 + -360 = 0 0 + -432x + x2 = 0 + -360 -432x + x2 = 0 + -360 Combine like terms: 0 + -360 = -360 -432x + x2 = -360 The x term is -432x. Take half its coefficient (-216). Square it (46656) and add it to both sides. Add '46656' to each side of the equation. -432x + 46656 + x2 = -360 + 46656 Reorder the terms: 46656 + -432x + x2 = -360 + 46656 Combine like terms: -360 + 46656 = 46296 46656 + -432x + x2 = 46296 Factor a perfect square on the left side: (x + -216)(x + -216) = 46296 Calculate the square root of the right side: 215.165052924 Break this problem into two subproblems by setting (x + -216) equal to 215.165052924 and -215.165052924.Subproblem 1
x + -216 = 215.165052924 Simplifying x + -216 = 215.165052924 Reorder the terms: -216 + x = 215.165052924 Solving -216 + x = 215.165052924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '216' to each side of the equation. -216 + 216 + x = 215.165052924 + 216 Combine like terms: -216 + 216 = 0 0 + x = 215.165052924 + 216 x = 215.165052924 + 216 Combine like terms: 215.165052924 + 216 = 431.165052924 x = 431.165052924 Simplifying x = 431.165052924Subproblem 2
x + -216 = -215.165052924 Simplifying x + -216 = -215.165052924 Reorder the terms: -216 + x = -215.165052924 Solving -216 + x = -215.165052924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '216' to each side of the equation. -216 + 216 + x = -215.165052924 + 216 Combine like terms: -216 + 216 = 0 0 + x = -215.165052924 + 216 x = -215.165052924 + 216 Combine like terms: -215.165052924 + 216 = 0.834947076 x = 0.834947076 Simplifying x = 0.834947076Solution
The solution to the problem is based on the solutions from the subproblems. x = {431.165052924, 0.834947076}
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