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Simplifying 8r2 + 16r + 29 = 9 Reorder the terms: 29 + 16r + 8r2 = 9 Solving 29 + 16r + 8r2 = 9 Solving for variable 'r'. Reorder the terms: 29 + -9 + 16r + 8r2 = 9 + -9 Combine like terms: 29 + -9 = 20 20 + 16r + 8r2 = 9 + -9 Combine like terms: 9 + -9 = 0 20 + 16r + 8r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 4r + 2r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 4r + 2r2)' equal to zero and attempt to solve: Simplifying 5 + 4r + 2r2 = 0 Solving 5 + 4r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 2r + r2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2r + -2.5 + r2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2r + r2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2r + r2 = 0 + -2.5 2r + r2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2r + r2 = -2.5 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = -2.5 + 1 Reorder the terms: 1 + 2r + r2 = -2.5 + 1 Combine like terms: -2.5 + 1 = -1.5 1 + 2r + r2 = -1.5 Factor a perfect square on the left side: (r + 1)(r + 1) = -1.5 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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