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Simplifying 0 = 64r2 + r + 10000 Reorder the terms: 0 = 10000 + r + 64r2 Solving 0 = 10000 + r + 64r2 Solving for variable 'r'. Combine like terms: 0 + -10000 = -10000 -10000 + -1r + -64r2 = 10000 + r + 64r2 + -10000 + -1r + -64r2 Reorder the terms: -10000 + -1r + -64r2 = 10000 + -10000 + r + -1r + 64r2 + -64r2 Combine like terms: 10000 + -10000 = 0 -10000 + -1r + -64r2 = 0 + r + -1r + 64r2 + -64r2 -10000 + -1r + -64r2 = r + -1r + 64r2 + -64r2 Combine like terms: r + -1r = 0 -10000 + -1r + -64r2 = 0 + 64r2 + -64r2 -10000 + -1r + -64r2 = 64r2 + -64r2 Combine like terms: 64r2 + -64r2 = 0 -10000 + -1r + -64r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10000 + r + 64r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10000 + r + 64r2)' equal to zero and attempt to solve: Simplifying 10000 + r + 64r2 = 0 Solving 10000 + r + 64r2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 156.25 + 0.015625r + r2 = 0 Move the constant term to the right: Add '-156.25' to each side of the equation. 156.25 + 0.015625r + -156.25 + r2 = 0 + -156.25 Reorder the terms: 156.25 + -156.25 + 0.015625r + r2 = 0 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + 0.015625r + r2 = 0 + -156.25 0.015625r + r2 = 0 + -156.25 Combine like terms: 0 + -156.25 = -156.25 0.015625r + r2 = -156.25 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. 0.015625r + 0.25 + r2 = -156.25 + 0.25 Reorder the terms: 0.25 + 0.015625r + r2 = -156.25 + 0.25 Combine like terms: -156.25 + 0.25 = -156 0.25 + 0.015625r + r2 = -156 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -156 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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