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Simplifying -16x2 + -64x + 60 = x Reorder the terms: 60 + -64x + -16x2 = x Solving 60 + -64x + -16x2 = x Solving for variable 'x'. Reorder the terms: 60 + -64x + -1x + -16x2 = x + -1x Combine like terms: -64x + -1x = -65x 60 + -65x + -16x2 = x + -1x Combine like terms: x + -1x = 0 60 + -65x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -3.75 + 4.0625x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 4.0625x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 4.0625x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 4.0625x + x2 = 0 + 3.75 4.0625x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 4.0625x + x2 = 3.75 The x term is 4.0625x. Take half its coefficient (2.03125). Square it (4.125976563) and add it to both sides. Add '4.125976563' to each side of the equation. 4.0625x + 4.125976563 + x2 = 3.75 + 4.125976563 Reorder the terms: 4.125976563 + 4.0625x + x2 = 3.75 + 4.125976563 Combine like terms: 3.75 + 4.125976563 = 7.875976563 4.125976563 + 4.0625x + x2 = 7.875976563 Factor a perfect square on the left side: (x + 2.03125)(x + 2.03125) = 7.875976563 Calculate the square root of the right side: 2.806417033 Break this problem into two subproblems by setting (x + 2.03125) equal to 2.806417033 and -2.806417033.Subproblem 1
x + 2.03125 = 2.806417033 Simplifying x + 2.03125 = 2.806417033 Reorder the terms: 2.03125 + x = 2.806417033 Solving 2.03125 + x = 2.806417033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.03125' to each side of the equation. 2.03125 + -2.03125 + x = 2.806417033 + -2.03125 Combine like terms: 2.03125 + -2.03125 = 0.00000 0.00000 + x = 2.806417033 + -2.03125 x = 2.806417033 + -2.03125 Combine like terms: 2.806417033 + -2.03125 = 0.775167033 x = 0.775167033 Simplifying x = 0.775167033Subproblem 2
x + 2.03125 = -2.806417033 Simplifying x + 2.03125 = -2.806417033 Reorder the terms: 2.03125 + x = -2.806417033 Solving 2.03125 + x = -2.806417033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.03125' to each side of the equation. 2.03125 + -2.03125 + x = -2.806417033 + -2.03125 Combine like terms: 2.03125 + -2.03125 = 0.00000 0.00000 + x = -2.806417033 + -2.03125 x = -2.806417033 + -2.03125 Combine like terms: -2.806417033 + -2.03125 = -4.837667033 x = -4.837667033 Simplifying x = -4.837667033Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.775167033, -4.837667033}
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