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Simplifying 8 = r(r + 4) Reorder the terms: 8 = r(4 + r) 8 = (4 * r + r * r) 8 = (4r + r2) Solving 8 = 4r + r2 Solving for variable 'r'. Reorder the terms: 8 + -4r + -1r2 = 4r + -4r + r2 + -1r2 Combine like terms: 4r + -4r = 0 8 + -4r + -1r2 = 0 + r2 + -1r2 8 + -4r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 8 + -4r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 4r + r2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 4r + 8 + r2 = 0 + 8 Reorder the terms: -8 + 8 + 4r + r2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4r + r2 = 0 + 8 4r + r2 = 0 + 8 Combine like terms: 0 + 8 = 8 4r + r2 = 8 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 8 + 4 Reorder the terms: 4 + 4r + r2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4r + r2 = 12 Factor a perfect square on the left side: (r + 2)(r + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (r + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
r + 2 = 3.464101615 Simplifying r + 2 = 3.464101615 Reorder the terms: 2 + r = 3.464101615 Solving 2 + r = 3.464101615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + r = 3.464101615 + -2 r = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 r = 1.464101615 Simplifying r = 1.464101615Subproblem 2
r + 2 = -3.464101615 Simplifying r + 2 = -3.464101615 Reorder the terms: 2 + r = -3.464101615 Solving 2 + r = -3.464101615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + r = -3.464101615 + -2 r = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 r = -5.464101615 Simplifying r = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.464101615, -5.464101615}
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