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Simplifying -16x2 + 12x = 146 Reorder the terms: 12x + -16x2 = 146 Solving 12x + -16x2 = 146 Solving for variable 'x'. Reorder the terms: -146 + 12x + -16x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + 12x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-73 + 6x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-73 + 6x + -8x2)' equal to zero and attempt to solve: Simplifying -73 + 6x + -8x2 = 0 Solving -73 + 6x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 9.125 + -0.75x + x2 = 0 Move the constant term to the right: Add '-9.125' to each side of the equation. 9.125 + -0.75x + -9.125 + x2 = 0 + -9.125 Reorder the terms: 9.125 + -9.125 + -0.75x + x2 = 0 + -9.125 Combine like terms: 9.125 + -9.125 = 0.000 0.000 + -0.75x + x2 = 0 + -9.125 -0.75x + x2 = 0 + -9.125 Combine like terms: 0 + -9.125 = -9.125 -0.75x + x2 = -9.125 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -9.125 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -9.125 + 0.140625 Combine like terms: -9.125 + 0.140625 = -8.984375 0.140625 + -0.75x + x2 = -8.984375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -8.984375 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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