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Simplifying 2f(5f + -2) + -10(f2 + -3f + 6) = 8f(f + 4) + 4(2f2 + -7f) Reorder the terms: 2f(-2 + 5f) + -10(f2 + -3f + 6) = 8f(f + 4) + 4(2f2 + -7f) (-2 * 2f + 5f * 2f) + -10(f2 + -3f + 6) = 8f(f + 4) + 4(2f2 + -7f) (-4f + 10f2) + -10(f2 + -3f + 6) = 8f(f + 4) + 4(2f2 + -7f) Reorder the terms: -4f + 10f2 + -10(6 + -3f + f2) = 8f(f + 4) + 4(2f2 + -7f) -4f + 10f2 + (6 * -10 + -3f * -10 + f2 * -10) = 8f(f + 4) + 4(2f2 + -7f) -4f + 10f2 + (-60 + 30f + -10f2) = 8f(f + 4) + 4(2f2 + -7f) Reorder the terms: -60 + -4f + 30f + 10f2 + -10f2 = 8f(f + 4) + 4(2f2 + -7f) Combine like terms: -4f + 30f = 26f -60 + 26f + 10f2 + -10f2 = 8f(f + 4) + 4(2f2 + -7f) Combine like terms: 10f2 + -10f2 = 0 -60 + 26f + 0 = 8f(f + 4) + 4(2f2 + -7f) -60 + 26f = 8f(f + 4) + 4(2f2 + -7f) Reorder the terms: -60 + 26f = 8f(4 + f) + 4(2f2 + -7f) -60 + 26f = (4 * 8f + f * 8f) + 4(2f2 + -7f) -60 + 26f = (32f + 8f2) + 4(2f2 + -7f) Reorder the terms: -60 + 26f = 32f + 8f2 + 4(-7f + 2f2) -60 + 26f = 32f + 8f2 + (-7f * 4 + 2f2 * 4) -60 + 26f = 32f + 8f2 + (-28f + 8f2) Reorder the terms: -60 + 26f = 32f + -28f + 8f2 + 8f2 Combine like terms: 32f + -28f = 4f -60 + 26f = 4f + 8f2 + 8f2 Combine like terms: 8f2 + 8f2 = 16f2 -60 + 26f = 4f + 16f2 Solving -60 + 26f = 4f + 16f2 Solving for variable 'f'. Combine like terms: 26f + -4f = 22f -60 + 22f + -16f2 = 4f + 16f2 + -4f + -16f2 Reorder the terms: -60 + 22f + -16f2 = 4f + -4f + 16f2 + -16f2 Combine like terms: 4f + -4f = 0 -60 + 22f + -16f2 = 0 + 16f2 + -16f2 -60 + 22f + -16f2 = 16f2 + -16f2 Combine like terms: 16f2 + -16f2 = 0 -60 + 22f + -16f2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + 11f + -8f2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + 11f + -8f2)' equal to zero and attempt to solve: Simplifying -30 + 11f + -8f2 = 0 Solving -30 + 11f + -8f2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 3.75 + -1.375f + f2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -1.375f + -3.75 + f2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -1.375f + f2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -1.375f + f2 = 0 + -3.75 -1.375f + f2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -1.375f + f2 = -3.75 The f term is -1.375f. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375f + 0.47265625 + f2 = -3.75 + 0.47265625 Reorder the terms: 0.47265625 + -1.375f + f2 = -3.75 + 0.47265625 Combine like terms: -3.75 + 0.47265625 = -3.27734375 0.47265625 + -1.375f + f2 = -3.27734375 Factor a perfect square on the left side: (f + -0.6875)(f + -0.6875) = -3.27734375 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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