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Simplifying 9x2 + -18x + 85 = 10 Reorder the terms: 85 + -18x + 9x2 = 10 Solving 85 + -18x + 9x2 = 10 Solving for variable 'x'. Reorder the terms: 85 + -10 + -18x + 9x2 = 10 + -10 Combine like terms: 85 + -10 = 75 75 + -18x + 9x2 = 10 + -10 Combine like terms: 10 + -10 = 0 75 + -18x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -6x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(25 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying 25 + -6x + 3x2 = 0 Solving 25 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + -2x + -8.333333333 + x2 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + -2x + x2 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + -8.333333333 -2x + x2 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 -2x + x2 = -8.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -8.333333333 + 1 Reorder the terms: 1 + -2x + x2 = -8.333333333 + 1 Combine like terms: -8.333333333 + 1 = -7.333333333 1 + -2x + x2 = -7.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = -7.333333333 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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