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Simplifying 9 + 8r = 4r(r + -6) + 4r Reorder the terms: 9 + 8r = 4r(-6 + r) + 4r 9 + 8r = (-6 * 4r + r * 4r) + 4r 9 + 8r = (-24r + 4r2) + 4r Reorder the terms: 9 + 8r = -24r + 4r + 4r2 Combine like terms: -24r + 4r = -20r 9 + 8r = -20r + 4r2 Solving 9 + 8r = -20r + 4r2 Solving for variable 'r'. Combine like terms: 8r + 20r = 28r 9 + 28r + -4r2 = -20r + 4r2 + 20r + -4r2 Reorder the terms: 9 + 28r + -4r2 = -20r + 20r + 4r2 + -4r2 Combine like terms: -20r + 20r = 0 9 + 28r + -4r2 = 0 + 4r2 + -4r2 9 + 28r + -4r2 = 4r2 + -4r2 Combine like terms: 4r2 + -4r2 = 0 9 + 28r + -4r2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + -7r + r2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -7r + 2.25 + r2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -7r + r2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -7r + r2 = 0 + 2.25 -7r + r2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -7r + r2 = 2.25 The r term is -7r. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7r + 12.25 + r2 = 2.25 + 12.25 Reorder the terms: 12.25 + -7r + r2 = 2.25 + 12.25 Combine like terms: 2.25 + 12.25 = 14.5 12.25 + -7r + r2 = 14.5 Factor a perfect square on the left side: (r + -3.5)(r + -3.5) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (r + -3.5) equal to 3.807886553 and -3.807886553.Subproblem 1
r + -3.5 = 3.807886553 Simplifying r + -3.5 = 3.807886553 Reorder the terms: -3.5 + r = 3.807886553 Solving -3.5 + r = 3.807886553 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = 3.807886553 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 3.807886553 + 3.5 r = 3.807886553 + 3.5 Combine like terms: 3.807886553 + 3.5 = 7.307886553 r = 7.307886553 Simplifying r = 7.307886553Subproblem 2
r + -3.5 = -3.807886553 Simplifying r + -3.5 = -3.807886553 Reorder the terms: -3.5 + r = -3.807886553 Solving -3.5 + r = -3.807886553 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = -3.807886553 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -3.807886553 + 3.5 r = -3.807886553 + 3.5 Combine like terms: -3.807886553 + 3.5 = -0.307886553 r = -0.307886553 Simplifying r = -0.307886553Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.307886553, -0.307886553}
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