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Simplifying 9x2 + -42x + 81 = 18 + -9x2 Reorder the terms: 81 + -42x + 9x2 = 18 + -9x2 Solving 81 + -42x + 9x2 = 18 + -9x2 Solving for variable 'x'. Reorder the terms: 81 + -18 + -42x + 9x2 + 9x2 = 18 + -9x2 + -18 + 9x2 Combine like terms: 81 + -18 = 63 63 + -42x + 9x2 + 9x2 = 18 + -9x2 + -18 + 9x2 Combine like terms: 9x2 + 9x2 = 18x2 63 + -42x + 18x2 = 18 + -9x2 + -18 + 9x2 Reorder the terms: 63 + -42x + 18x2 = 18 + -18 + -9x2 + 9x2 Combine like terms: 18 + -18 = 0 63 + -42x + 18x2 = 0 + -9x2 + 9x2 63 + -42x + 18x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 63 + -42x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(21 + -14x + 6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(21 + -14x + 6x2)' equal to zero and attempt to solve: Simplifying 21 + -14x + 6x2 = 0 Solving 21 + -14x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.5 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -2.333333333x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -2.333333333x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -2.333333333x + x2 = 0 + -3.5 -2.333333333x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -2.333333333x + x2 = -3.5 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -3.5 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -3.5 + 1.361111112 Combine like terms: -3.5 + 1.361111112 = -2.138888888 1.361111112 + -2.333333333x + x2 = -2.138888888 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = -2.138888888 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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