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Simplifying 0 = -16x2 + 62x + 2 Reorder the terms: 0 = 2 + 62x + -16x2 Solving 0 = 2 + 62x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -62x + 16x2 = 2 + 62x + -16x2 + -2 + -62x + 16x2 Reorder the terms: -2 + -62x + 16x2 = 2 + -2 + 62x + -62x + -16x2 + 16x2 Combine like terms: 2 + -2 = 0 -2 + -62x + 16x2 = 0 + 62x + -62x + -16x2 + 16x2 -2 + -62x + 16x2 = 62x + -62x + -16x2 + 16x2 Combine like terms: 62x + -62x = 0 -2 + -62x + 16x2 = 0 + -16x2 + 16x2 -2 + -62x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2 + -62x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -31x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -31x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + -31x + 8x2 = 0 Solving -1 + -31x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -3.875x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.875x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.875x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.875x + x2 = 0 + 0.125 -3.875x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.875x + x2 = 0.125 The x term is -3.875x. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875x + 3.75390625 + x2 = 0.125 + 3.75390625 Reorder the terms: 3.75390625 + -3.875x + x2 = 0.125 + 3.75390625 Combine like terms: 0.125 + 3.75390625 = 3.87890625 3.75390625 + -3.875x + x2 = 3.87890625 Factor a perfect square on the left side: (x + -1.9375)(x + -1.9375) = 3.87890625 Calculate the square root of the right side: 1.969493907 Break this problem into two subproblems by setting (x + -1.9375) equal to 1.969493907 and -1.969493907.Subproblem 1
x + -1.9375 = 1.969493907 Simplifying x + -1.9375 = 1.969493907 Reorder the terms: -1.9375 + x = 1.969493907 Solving -1.9375 + x = 1.969493907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = 1.969493907 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = 1.969493907 + 1.9375 x = 1.969493907 + 1.9375 Combine like terms: 1.969493907 + 1.9375 = 3.906993907 x = 3.906993907 Simplifying x = 3.906993907Subproblem 2
x + -1.9375 = -1.969493907 Simplifying x + -1.9375 = -1.969493907 Reorder the terms: -1.9375 + x = -1.969493907 Solving -1.9375 + x = -1.969493907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = -1.969493907 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = -1.969493907 + 1.9375 x = -1.969493907 + 1.9375 Combine like terms: -1.969493907 + 1.9375 = -0.031993907 x = -0.031993907 Simplifying x = -0.031993907Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.906993907, -0.031993907}Solution
x = {3.906993907, -0.031993907}
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