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Simplifying x = -16x2 + 64x + 192 Reorder the terms: x = 192 + 64x + -16x2 Solving x = 192 + 64x + -16x2 Solving for variable 'x'. Reorder the terms: -192 + x + -64x + 16x2 = 192 + 64x + -16x2 + -192 + -64x + 16x2 Combine like terms: x + -64x = -63x -192 + -63x + 16x2 = 192 + 64x + -16x2 + -192 + -64x + 16x2 Reorder the terms: -192 + -63x + 16x2 = 192 + -192 + 64x + -64x + -16x2 + 16x2 Combine like terms: 192 + -192 = 0 -192 + -63x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -192 + -63x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -192 + -63x + 16x2 = 0 + -16x2 + 16x2 -192 + -63x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -192 + -63x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -12 + -3.9375x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -3.9375x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -3.9375x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3.9375x + x2 = 0 + 12 -3.9375x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3.9375x + x2 = 12 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 = 12 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = 12 + 3.875976563 Combine like terms: 12 + 3.875976563 = 15.875976563 3.875976563 + -3.9375x + x2 = 15.875976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 15.875976563 Calculate the square root of the right side: 3.984466911 Break this problem into two subproblems by setting (x + -1.96875) equal to 3.984466911 and -3.984466911.Subproblem 1
x + -1.96875 = 3.984466911 Simplifying x + -1.96875 = 3.984466911 Reorder the terms: -1.96875 + x = 3.984466911 Solving -1.96875 + x = 3.984466911 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 = 3.984466911 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 3.984466911 + 1.96875 x = 3.984466911 + 1.96875 Combine like terms: 3.984466911 + 1.96875 = 5.953216911 x = 5.953216911 Simplifying x = 5.953216911Subproblem 2
x + -1.96875 = -3.984466911 Simplifying x + -1.96875 = -3.984466911 Reorder the terms: -1.96875 + x = -3.984466911 Solving -1.96875 + x = -3.984466911 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 = -3.984466911 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -3.984466911 + 1.96875 x = -3.984466911 + 1.96875 Combine like terms: -3.984466911 + 1.96875 = -2.015716911 x = -2.015716911 Simplifying x = -2.015716911Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.953216911, -2.015716911}
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