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Simplifying 3 + -1x = 121 + 9x2 + -66 Reorder the terms: 3 + -1x = 121 + -66 + 9x2 Combine like terms: 121 + -66 = 55 3 + -1x = 55 + 9x2 Solving 3 + -1x = 55 + 9x2 Solving for variable 'x'. Reorder the terms: 3 + -55 + -1x + -9x2 = 55 + 9x2 + -55 + -9x2 Combine like terms: 3 + -55 = -52 -52 + -1x + -9x2 = 55 + 9x2 + -55 + -9x2 Reorder the terms: -52 + -1x + -9x2 = 55 + -55 + 9x2 + -9x2 Combine like terms: 55 + -55 = 0 -52 + -1x + -9x2 = 0 + 9x2 + -9x2 -52 + -1x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -52 + -1x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(52 + x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(52 + x + 9x2)' equal to zero and attempt to solve: Simplifying 52 + x + 9x2 = 0 Solving 52 + x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5.777777778 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-5.777777778' to each side of the equation. 5.777777778 + 0.1111111111x + -5.777777778 + x2 = 0 + -5.777777778 Reorder the terms: 5.777777778 + -5.777777778 + 0.1111111111x + x2 = 0 + -5.777777778 Combine like terms: 5.777777778 + -5.777777778 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + -5.777777778 0.1111111111x + x2 = 0 + -5.777777778 Combine like terms: 0 + -5.777777778 = -5.777777778 0.1111111111x + x2 = -5.777777778 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = -5.777777778 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = -5.777777778 + 0.25 Combine like terms: -5.777777778 + 0.25 = -5.527777778 0.25 + 0.1111111111x + x2 = -5.527777778 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -5.527777778 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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