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Simplifying 16(14x + 12) + -1x(16 + 14x) + -2x(15 + -30x) = 46(1x + -2) Reorder the terms: 16(12 + 14x) + -1x(16 + 14x) + -2x(15 + -30x) = 46(1x + -2) (12 * 16 + 14x * 16) + -1x(16 + 14x) + -2x(15 + -30x) = 46(1x + -2) (192 + 224x) + -1x(16 + 14x) + -2x(15 + -30x) = 46(1x + -2) 192 + 224x + (16 * -1x + 14x * -1x) + -2x(15 + -30x) = 46(1x + -2) 192 + 224x + (-16x + -14x2) + -2x(15 + -30x) = 46(1x + -2) 192 + 224x + -16x + -14x2 + (15 * -2x + -30x * -2x) = 46(1x + -2) 192 + 224x + -16x + -14x2 + (-30x + 60x2) = 46(1x + -2) Reorder the terms: 192 + 224x + -16x + -30x + -14x2 + 60x2 = 46(1x + -2) Combine like terms: 224x + -16x = 208x 192 + 208x + -30x + -14x2 + 60x2 = 46(1x + -2) Combine like terms: 208x + -30x = 178x 192 + 178x + -14x2 + 60x2 = 46(1x + -2) Combine like terms: -14x2 + 60x2 = 46x2 192 + 178x + 46x2 = 46(1x + -2) Reorder the terms: 192 + 178x + 46x2 = 46(-2 + 1x) 192 + 178x + 46x2 = (-2 * 46 + 1x * 46) 192 + 178x + 46x2 = (-92 + 46x) Solving 192 + 178x + 46x2 = -92 + 46x Solving for variable 'x'. Reorder the terms: 192 + 92 + 178x + -46x + 46x2 = -92 + 46x + 92 + -46x Combine like terms: 192 + 92 = 284 284 + 178x + -46x + 46x2 = -92 + 46x + 92 + -46x Combine like terms: 178x + -46x = 132x 284 + 132x + 46x2 = -92 + 46x + 92 + -46x Reorder the terms: 284 + 132x + 46x2 = -92 + 92 + 46x + -46x Combine like terms: -92 + 92 = 0 284 + 132x + 46x2 = 0 + 46x + -46x 284 + 132x + 46x2 = 46x + -46x Combine like terms: 46x + -46x = 0 284 + 132x + 46x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(142 + 66x + 23x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(142 + 66x + 23x2)' equal to zero and attempt to solve: Simplifying 142 + 66x + 23x2 = 0 Solving 142 + 66x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 6.173913043 + 2.869565217x + x2 = 0 Move the constant term to the right: Add '-6.173913043' to each side of the equation. 6.173913043 + 2.869565217x + -6.173913043 + x2 = 0 + -6.173913043 Reorder the terms: 6.173913043 + -6.173913043 + 2.869565217x + x2 = 0 + -6.173913043 Combine like terms: 6.173913043 + -6.173913043 = 0.000000000 0.000000000 + 2.869565217x + x2 = 0 + -6.173913043 2.869565217x + x2 = 0 + -6.173913043 Combine like terms: 0 + -6.173913043 = -6.173913043 2.869565217x + x2 = -6.173913043 The x term is 2.869565217x. Take half its coefficient (1.434782609). Square it (2.058601135) and add it to both sides. Add '2.058601135' to each side of the equation. 2.869565217x + 2.058601135 + x2 = -6.173913043 + 2.058601135 Reorder the terms: 2.058601135 + 2.869565217x + x2 = -6.173913043 + 2.058601135 Combine like terms: -6.173913043 + 2.058601135 = -4.115311908 2.058601135 + 2.869565217x + x2 = -4.115311908 Factor a perfect square on the left side: (x + 1.434782609)(x + 1.434782609) = -4.115311908 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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