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Simplifying -5r2 + -1r + 5 = 10 Reorder the terms: 5 + -1r + -5r2 = 10 Solving 5 + -1r + -5r2 = 10 Solving for variable 'r'. Reorder the terms: 5 + -10 + -1r + -5r2 = 10 + -10 Combine like terms: 5 + -10 = -5 -5 + -1r + -5r2 = 10 + -10 Combine like terms: 10 + -10 = 0 -5 + -1r + -5r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + r + 5r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + r + 5r2)' equal to zero and attempt to solve: Simplifying 5 + r + 5r2 = 0 Solving 5 + r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 0.2r + r2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.2r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + 0.2r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.2r + r2 = 0 + -1 0.2r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.2r + r2 = -1 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. 0.2r + 0.25 + r2 = -1 + 0.25 Reorder the terms: 0.25 + 0.2r + r2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.2r + r2 = -0.75 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -0.75 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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