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Simplifying x + 2 = 9x2 + 60x + 100 Reorder the terms: 2 + x = 9x2 + 60x + 100 Reorder the terms: 2 + x = 100 + 60x + 9x2 Solving 2 + x = 100 + 60x + 9x2 Solving for variable 'x'. Reorder the terms: 2 + -100 + x + -60x + -9x2 = 100 + 60x + 9x2 + -100 + -60x + -9x2 Combine like terms: 2 + -100 = -98 -98 + x + -60x + -9x2 = 100 + 60x + 9x2 + -100 + -60x + -9x2 Combine like terms: x + -60x = -59x -98 + -59x + -9x2 = 100 + 60x + 9x2 + -100 + -60x + -9x2 Reorder the terms: -98 + -59x + -9x2 = 100 + -100 + 60x + -60x + 9x2 + -9x2 Combine like terms: 100 + -100 = 0 -98 + -59x + -9x2 = 0 + 60x + -60x + 9x2 + -9x2 -98 + -59x + -9x2 = 60x + -60x + 9x2 + -9x2 Combine like terms: 60x + -60x = 0 -98 + -59x + -9x2 = 0 + 9x2 + -9x2 -98 + -59x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -98 + -59x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(98 + 59x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(98 + 59x + 9x2)' equal to zero and attempt to solve: Simplifying 98 + 59x + 9x2 = 0 Solving 98 + 59x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 10.88888889 + 6.555555556x + x2 = 0 Move the constant term to the right: Add '-10.88888889' to each side of the equation. 10.88888889 + 6.555555556x + -10.88888889 + x2 = 0 + -10.88888889 Reorder the terms: 10.88888889 + -10.88888889 + 6.555555556x + x2 = 0 + -10.88888889 Combine like terms: 10.88888889 + -10.88888889 = 0.00000000 0.00000000 + 6.555555556x + x2 = 0 + -10.88888889 6.555555556x + x2 = 0 + -10.88888889 Combine like terms: 0 + -10.88888889 = -10.88888889 6.555555556x + x2 = -10.88888889 The x term is 6.555555556x. Take half its coefficient (3.277777778). Square it (10.74382716) and add it to both sides. Add '10.74382716' to each side of the equation. 6.555555556x + 10.74382716 + x2 = -10.88888889 + 10.74382716 Reorder the terms: 10.74382716 + 6.555555556x + x2 = -10.88888889 + 10.74382716 Combine like terms: -10.88888889 + 10.74382716 = -0.14506173 10.74382716 + 6.555555556x + x2 = -0.14506173 Factor a perfect square on the left side: (x + 3.277777778)(x + 3.277777778) = -0.14506173 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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