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Simplifying 0 = -9x2 + 21x + -18 Reorder the terms: 0 = -18 + 21x + -9x2 Solving 0 = -18 + 21x + -9x2 Solving for variable 'x'. Combine like terms: 0 + 18 = 18 18 + -21x + 9x2 = -18 + 21x + -9x2 + 18 + -21x + 9x2 Reorder the terms: 18 + -21x + 9x2 = -18 + 18 + 21x + -21x + -9x2 + 9x2 Combine like terms: -18 + 18 = 0 18 + -21x + 9x2 = 0 + 21x + -21x + -9x2 + 9x2 18 + -21x + 9x2 = 21x + -21x + -9x2 + 9x2 Combine like terms: 21x + -21x = 0 18 + -21x + 9x2 = 0 + -9x2 + 9x2 18 + -21x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 18 + -21x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -7x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + -7x + 3x2 = 0 Solving 6 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.333333333x + x2 = 0 + -2 -2.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.333333333x + x2 = -2 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 = -2 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -2 + 1.361111112 Combine like terms: -2 + 1.361111112 = -0.638888888 1.361111112 + -2.333333333x + x2 = -0.638888888 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = -0.638888888 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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