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Simplifying 2r2 + -10r + 40 = 0 Reorder the terms: 40 + -10r + 2r2 = 0 Solving 40 + -10r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -5r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -5r + r2)' equal to zero and attempt to solve: Simplifying 20 + -5r + r2 = 0 Solving 20 + -5r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -5r + -20 + r2 = 0 + -20 Reorder the terms: 20 + -20 + -5r + r2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -5r + r2 = 0 + -20 -5r + r2 = 0 + -20 Combine like terms: 0 + -20 = -20 -5r + r2 = -20 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = -20 + 6.25 Reorder the terms: 6.25 + -5r + r2 = -20 + 6.25 Combine like terms: -20 + 6.25 = -13.75 6.25 + -5r + r2 = -13.75 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = -13.75 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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