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Simplifying x = -16x2 + 64x + 160 Reorder the terms: x = 160 + 64x + -16x2 Solving x = 160 + 64x + -16x2 Solving for variable 'x'. Reorder the terms: -160 + x + -64x + 16x2 = 160 + 64x + -16x2 + -160 + -64x + 16x2 Combine like terms: x + -64x = -63x -160 + -63x + 16x2 = 160 + 64x + -16x2 + -160 + -64x + 16x2 Reorder the terms: -160 + -63x + 16x2 = 160 + -160 + 64x + -64x + -16x2 + 16x2 Combine like terms: 160 + -160 = 0 -160 + -63x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -160 + -63x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -160 + -63x + 16x2 = 0 + -16x2 + 16x2 -160 + -63x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -160 + -63x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10 + -3.9375x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -3.9375x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -3.9375x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3.9375x + x2 = 0 + 10 -3.9375x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3.9375x + x2 = 10 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = 10 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = 10 + 3.875976563 Combine like terms: 10 + 3.875976563 = 13.875976563 3.875976563 + -3.9375x + x2 = 13.875976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 13.875976563 Calculate the square root of the right side: 3.725047189 Break this problem into two subproblems by setting (x + -1.96875) equal to 3.725047189 and -3.725047189.Subproblem 1
x + -1.96875 = 3.725047189 Simplifying x + -1.96875 = 3.725047189 Reorder the terms: -1.96875 + x = 3.725047189 Solving -1.96875 + x = 3.725047189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 3.725047189 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 3.725047189 + 1.96875 x = 3.725047189 + 1.96875 Combine like terms: 3.725047189 + 1.96875 = 5.693797189 x = 5.693797189 Simplifying x = 5.693797189Subproblem 2
x + -1.96875 = -3.725047189 Simplifying x + -1.96875 = -3.725047189 Reorder the terms: -1.96875 + x = -3.725047189 Solving -1.96875 + x = -3.725047189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -3.725047189 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -3.725047189 + 1.96875 x = -3.725047189 + 1.96875 Combine like terms: -3.725047189 + 1.96875 = -1.756297189 x = -1.756297189 Simplifying x = -1.756297189Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.693797189, -1.756297189}
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