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Simplifying x = -16x2 + 96x + 640 Reorder the terms: x = 640 + 96x + -16x2 Solving x = 640 + 96x + -16x2 Solving for variable 'x'. Reorder the terms: -640 + x + -96x + 16x2 = 640 + 96x + -16x2 + -640 + -96x + 16x2 Combine like terms: x + -96x = -95x -640 + -95x + 16x2 = 640 + 96x + -16x2 + -640 + -96x + 16x2 Reorder the terms: -640 + -95x + 16x2 = 640 + -640 + 96x + -96x + -16x2 + 16x2 Combine like terms: 640 + -640 = 0 -640 + -95x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -640 + -95x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -640 + -95x + 16x2 = 0 + -16x2 + 16x2 -640 + -95x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -640 + -95x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -40 + -5.9375x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -5.9375x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -5.9375x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -5.9375x + x2 = 0 + 40 -5.9375x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -5.9375x + x2 = 40 The x term is -5.9375x. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375x + 8.813476563 + x2 = 40 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375x + x2 = 40 + 8.813476563 Combine like terms: 40 + 8.813476563 = 48.813476563 8.813476563 + -5.9375x + x2 = 48.813476563 Factor a perfect square on the left side: (x + -2.96875)(x + -2.96875) = 48.813476563 Calculate the square root of the right side: 6.986664194 Break this problem into two subproblems by setting (x + -2.96875) equal to 6.986664194 and -6.986664194.Subproblem 1
x + -2.96875 = 6.986664194 Simplifying x + -2.96875 = 6.986664194 Reorder the terms: -2.96875 + x = 6.986664194 Solving -2.96875 + x = 6.986664194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = 6.986664194 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = 6.986664194 + 2.96875 x = 6.986664194 + 2.96875 Combine like terms: 6.986664194 + 2.96875 = 9.955414194 x = 9.955414194 Simplifying x = 9.955414194Subproblem 2
x + -2.96875 = -6.986664194 Simplifying x + -2.96875 = -6.986664194 Reorder the terms: -2.96875 + x = -6.986664194 Solving -2.96875 + x = -6.986664194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = -6.986664194 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = -6.986664194 + 2.96875 x = -6.986664194 + 2.96875 Combine like terms: -6.986664194 + 2.96875 = -4.017914194 x = -4.017914194 Simplifying x = -4.017914194Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.955414194, -4.017914194}
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