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Simplifying 18x + -2x2 = 150 Solving 18x + -2x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 18x + -2x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 18x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 9x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying -75 + 9x + -1x2 = 0 Solving -75 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 75 + -9x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -9x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -9x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -9x + x2 = 0 + -75 -9x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -9x + x2 = -75 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 = -75 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -75 + 20.25 Combine like terms: -75 + 20.25 = -54.75 20.25 + -9x + x2 = -54.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -54.75 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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