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Simplifying 20x2 + -180x + 975 = 0 Reorder the terms: 975 + -180x + 20x2 = 0 Solving 975 + -180x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(195 + -36x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(195 + -36x + 4x2)' equal to zero and attempt to solve: Simplifying 195 + -36x + 4x2 = 0 Solving 195 + -36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 48.75 + -9x + x2 = 0 Move the constant term to the right: Add '-48.75' to each side of the equation. 48.75 + -9x + -48.75 + x2 = 0 + -48.75 Reorder the terms: 48.75 + -48.75 + -9x + x2 = 0 + -48.75 Combine like terms: 48.75 + -48.75 = 0.00 0.00 + -9x + x2 = 0 + -48.75 -9x + x2 = 0 + -48.75 Combine like terms: 0 + -48.75 = -48.75 -9x + x2 = -48.75 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 = -48.75 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -48.75 + 20.25 Combine like terms: -48.75 + 20.25 = -28.5 20.25 + -9x + x2 = -28.5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -28.5 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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