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Simplifying -16x2 + 50x + 6 = 0 Reorder the terms: 6 + 50x + -16x2 = 0 Solving 6 + 50x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 25x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 25x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 25x + -8x2 = 0 Solving 3 + 25x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.125x + x2 = 0 + 0.375 -3.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.125x + x2 = 0.375 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 0.375 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.375 + 2.44140625 Combine like terms: 0.375 + 2.44140625 = 2.81640625 2.44140625 + -3.125x + x2 = 2.81640625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.81640625 Calculate the square root of the right side: 1.678215198 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.678215198 and -1.678215198.Subproblem 1
x + -1.5625 = 1.678215198 Simplifying x + -1.5625 = 1.678215198 Reorder the terms: -1.5625 + x = 1.678215198 Solving -1.5625 + x = 1.678215198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.678215198 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.678215198 + 1.5625 x = 1.678215198 + 1.5625 Combine like terms: 1.678215198 + 1.5625 = 3.240715198 x = 3.240715198 Simplifying x = 3.240715198Subproblem 2
x + -1.5625 = -1.678215198 Simplifying x + -1.5625 = -1.678215198 Reorder the terms: -1.5625 + x = -1.678215198 Solving -1.5625 + x = -1.678215198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.678215198 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.678215198 + 1.5625 x = -1.678215198 + 1.5625 Combine like terms: -1.678215198 + 1.5625 = -0.115715198 x = -0.115715198 Simplifying x = -0.115715198Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.240715198, -0.115715198}Solution
x = {3.240715198, -0.115715198}
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