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Simplifying x = 16x2 + 64x + 60 Reorder the terms: x = 60 + 64x + 16x2 Solving x = 60 + 64x + 16x2 Solving for variable 'x'. Reorder the terms: -60 + x + -64x + -16x2 = 60 + 64x + 16x2 + -60 + -64x + -16x2 Combine like terms: x + -64x = -63x -60 + -63x + -16x2 = 60 + 64x + 16x2 + -60 + -64x + -16x2 Reorder the terms: -60 + -63x + -16x2 = 60 + -60 + 64x + -64x + 16x2 + -16x2 Combine like terms: 60 + -60 = 0 -60 + -63x + -16x2 = 0 + 64x + -64x + 16x2 + -16x2 -60 + -63x + -16x2 = 64x + -64x + 16x2 + -16x2 Combine like terms: 64x + -64x = 0 -60 + -63x + -16x2 = 0 + 16x2 + -16x2 -60 + -63x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -60 + -63x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 63x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 63x + 16x2)' equal to zero and attempt to solve: Simplifying 60 + 63x + 16x2 = 0 Solving 60 + 63x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.75 + 3.9375x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 3.9375x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 3.9375x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 3.9375x + x2 = 0 + -3.75 3.9375x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 3.9375x + x2 = -3.75 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 = -3.75 + 3.875976563 Reorder the terms: 3.875976563 + 3.9375x + x2 = -3.75 + 3.875976563 Combine like terms: -3.75 + 3.875976563 = 0.125976563 3.875976563 + 3.9375x + x2 = 0.125976563 Factor a perfect square on the left side: (x + 1.96875)(x + 1.96875) = 0.125976563 Calculate the square root of the right side: 0.354931772 Break this problem into two subproblems by setting (x + 1.96875) equal to 0.354931772 and -0.354931772.Subproblem 1
x + 1.96875 = 0.354931772 Simplifying x + 1.96875 = 0.354931772 Reorder the terms: 1.96875 + x = 0.354931772 Solving 1.96875 + x = 0.354931772 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 = 0.354931772 + -1.96875 Combine like terms: 1.96875 + -1.96875 = 0.00000 0.00000 + x = 0.354931772 + -1.96875 x = 0.354931772 + -1.96875 Combine like terms: 0.354931772 + -1.96875 = -1.613818228 x = -1.613818228 Simplifying x = -1.613818228Subproblem 2
x + 1.96875 = -0.354931772 Simplifying x + 1.96875 = -0.354931772 Reorder the terms: 1.96875 + x = -0.354931772 Solving 1.96875 + x = -0.354931772 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 = -0.354931772 + -1.96875 Combine like terms: 1.96875 + -1.96875 = 0.00000 0.00000 + x = -0.354931772 + -1.96875 x = -0.354931772 + -1.96875 Combine like terms: -0.354931772 + -1.96875 = -2.323681772 x = -2.323681772 Simplifying x = -2.323681772Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.613818228, -2.323681772}Solution
x = {-1.613818228, -2.323681772}
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