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Simplifying 4r5(4r2 + 4r + 5) = 0 Reorder the terms: 4r5(5 + 4r + 4r2) = 0 (5 * 4r5 + 4r * 4r5 + 4r2 * 4r5) = 0 (20r5 + 16r6 + 16r7) = 0 Solving 20r5 + 16r6 + 16r7 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4r5'. 4r5(5 + 4r + 4r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'r5' equal to zero and attempt to solve: Simplifying r5 = 0 Solving r5 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + 4r + 4r2)' equal to zero and attempt to solve: Simplifying 5 + 4r + 4r2 = 0 Solving 5 + 4r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + r + r2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + r + -1.25 + r2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + r + r2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + r + r2 = 0 + -1.25 r + r2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 r + r2 = -1.25 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = -1.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = -1.25 + 0.25 Combine like terms: -1.25 + 0.25 = -1 1.25 + r2 = -1 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -1 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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