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Simplifying 0 = 130 + -6x + -16x2 Solving 0 = 130 + -6x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -130 = -130 -130 + 6x + 16x2 = 130 + -6x + -16x2 + -130 + 6x + 16x2 Reorder the terms: -130 + 6x + 16x2 = 130 + -130 + -6x + 6x + -16x2 + 16x2 Combine like terms: 130 + -130 = 0 -130 + 6x + 16x2 = 0 + -6x + 6x + -16x2 + 16x2 -130 + 6x + 16x2 = -6x + 6x + -16x2 + 16x2 Combine like terms: -6x + 6x = 0 -130 + 6x + 16x2 = 0 + -16x2 + 16x2 -130 + 6x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -130 + 6x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 3x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying -65 + 3x + 8x2 = 0 Solving -65 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.125 + 0.375x + x2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 0.375x + 8.125 + x2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 0.375x + x2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 0.375x + x2 = 0 + 8.125 0.375x + x2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 0.375x + x2 = 8.125 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 8.125 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 8.125 + 0.03515625 Combine like terms: 8.125 + 0.03515625 = 8.16015625 0.03515625 + 0.375x + x2 = 8.16015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 8.16015625 Calculate the square root of the right side: 2.856598721 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.856598721 and -2.856598721.Subproblem 1
x + 0.1875 = 2.856598721 Simplifying x + 0.1875 = 2.856598721 Reorder the terms: 0.1875 + x = 2.856598721 Solving 0.1875 + x = 2.856598721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.856598721 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.856598721 + -0.1875 x = 2.856598721 + -0.1875 Combine like terms: 2.856598721 + -0.1875 = 2.669098721 x = 2.669098721 Simplifying x = 2.669098721Subproblem 2
x + 0.1875 = -2.856598721 Simplifying x + 0.1875 = -2.856598721 Reorder the terms: 0.1875 + x = -2.856598721 Solving 0.1875 + x = -2.856598721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.856598721 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.856598721 + -0.1875 x = -2.856598721 + -0.1875 Combine like terms: -2.856598721 + -0.1875 = -3.044098721 x = -3.044098721 Simplifying x = -3.044098721Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.669098721, -3.044098721}Solution
x = {2.669098721, -3.044098721}
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