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Simplifying 0 = 9x2 + -81x + 252 Reorder the terms: 0 = 252 + -81x + 9x2 Solving 0 = 252 + -81x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -252 = -252 -252 + 81x + -9x2 = 252 + -81x + 9x2 + -252 + 81x + -9x2 Reorder the terms: -252 + 81x + -9x2 = 252 + -252 + -81x + 81x + 9x2 + -9x2 Combine like terms: 252 + -252 = 0 -252 + 81x + -9x2 = 0 + -81x + 81x + 9x2 + -9x2 -252 + 81x + -9x2 = -81x + 81x + 9x2 + -9x2 Combine like terms: -81x + 81x = 0 -252 + 81x + -9x2 = 0 + 9x2 + -9x2 -252 + 81x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -252 + 81x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-28 + 9x + -1x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-28 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying -28 + 9x + -1x2 = 0 Solving -28 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 28 + -9x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -9x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -9x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -9x + x2 = 0 + -28 -9x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -9x + x2 = -28 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -28 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -28 + 20.25 Combine like terms: -28 + 20.25 = -7.75 20.25 + -9x + x2 = -7.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -7.75 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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