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Simplifying 0 = -16x2 + 44x + 6 Reorder the terms: 0 = 6 + 44x + -16x2 Solving 0 = 6 + 44x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -44x + 16x2 = 6 + 44x + -16x2 + -6 + -44x + 16x2 Reorder the terms: -6 + -44x + 16x2 = 6 + -6 + 44x + -44x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -44x + 16x2 = 0 + 44x + -44x + -16x2 + 16x2 -6 + -44x + 16x2 = 44x + -44x + -16x2 + 16x2 Combine like terms: 44x + -44x = 0 -6 + -44x + 16x2 = 0 + -16x2 + 16x2 -6 + -44x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -44x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -22x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -22x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -22x + 8x2 = 0 Solving -3 + -22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -2.75x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -2.75x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -2.75x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -2.75x + x2 = 0 + 0.375 -2.75x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -2.75x + x2 = 0.375 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 0.375 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 0.375 + 1.890625 Combine like terms: 0.375 + 1.890625 = 2.265625 1.890625 + -2.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + -1.375) equal to 1.505199322 and -1.505199322.Subproblem 1
x + -1.375 = 1.505199322 Simplifying x + -1.375 = 1.505199322 Reorder the terms: -1.375 + x = 1.505199322 Solving -1.375 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.505199322 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.505199322 + 1.375 x = 1.505199322 + 1.375 Combine like terms: 1.505199322 + 1.375 = 2.880199322 x = 2.880199322 Simplifying x = 2.880199322Subproblem 2
x + -1.375 = -1.505199322 Simplifying x + -1.375 = -1.505199322 Reorder the terms: -1.375 + x = -1.505199322 Solving -1.375 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.505199322 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.505199322 + 1.375 x = -1.505199322 + 1.375 Combine like terms: -1.505199322 + 1.375 = -0.130199322 x = -0.130199322 Simplifying x = -0.130199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.880199322, -0.130199322}Solution
x = {2.880199322, -0.130199322}
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