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Simplifying 4r2 + 4r + 18 = 10 Reorder the terms: 18 + 4r + 4r2 = 10 Solving 18 + 4r + 4r2 = 10 Solving for variable 'r'. Reorder the terms: 18 + -10 + 4r + 4r2 = 10 + -10 Combine like terms: 18 + -10 = 8 8 + 4r + 4r2 = 10 + -10 Combine like terms: 10 + -10 = 0 8 + 4r + 4r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + r + r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + r + r2)' equal to zero and attempt to solve: Simplifying 2 + r + r2 = 0 Solving 2 + r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + r + r2 = 0 + -2 r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 r + r2 = -2 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. r + 0.25 + r2 = -2 + 0.25 Reorder the terms: 0.25 + r + r2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + r + r2 = -1.75 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -1.75 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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