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Simplifying 0 = -16x2 + 60x + 6 Reorder the terms: 0 = 6 + 60x + -16x2 Solving 0 = 6 + 60x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -60x + 16x2 = 6 + 60x + -16x2 + -6 + -60x + 16x2 Reorder the terms: -6 + -60x + 16x2 = 6 + -6 + 60x + -60x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -60x + 16x2 = 0 + 60x + -60x + -16x2 + 16x2 -6 + -60x + 16x2 = 60x + -60x + -16x2 + 16x2 Combine like terms: 60x + -60x = 0 -6 + -60x + 16x2 = 0 + -16x2 + 16x2 -6 + -60x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -60x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -30x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -30x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -30x + 8x2 = 0 Solving -3 + -30x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -3.75x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.75x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.75x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.75x + x2 = 0 + 0.375 -3.75x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.75x + x2 = 0.375 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 0.375 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 0.375 + 3.515625 Combine like terms: 0.375 + 3.515625 = 3.890625 3.515625 + -3.75x + x2 = 3.890625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + -1.875) equal to 1.97246673 and -1.97246673.Subproblem 1
x + -1.875 = 1.97246673 Simplifying x + -1.875 = 1.97246673 Reorder the terms: -1.875 + x = 1.97246673 Solving -1.875 + x = 1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 1.97246673 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.97246673 + 1.875 x = 1.97246673 + 1.875 Combine like terms: 1.97246673 + 1.875 = 3.84746673 x = 3.84746673 Simplifying x = 3.84746673Subproblem 2
x + -1.875 = -1.97246673 Simplifying x + -1.875 = -1.97246673 Reorder the terms: -1.875 + x = -1.97246673 Solving -1.875 + x = -1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -1.97246673 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.97246673 + 1.875 x = -1.97246673 + 1.875 Combine like terms: -1.97246673 + 1.875 = -0.09746673 x = -0.09746673 Simplifying x = -0.09746673Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.84746673, -0.09746673}Solution
x = {3.84746673, -0.09746673}
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