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Simplifying 400 = r(12 + r) 400 = (12 * r + r * r) 400 = (12r + r2) Solving 400 = 12r + r2 Solving for variable 'r'. Reorder the terms: 400 + -12r + -1r2 = 12r + -12r + r2 + -1r2 Combine like terms: 12r + -12r = 0 400 + -12r + -1r2 = 0 + r2 + -1r2 400 + -12r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 400 + -12r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -400 + 12r + r2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + 12r + 400 + r2 = 0 + 400 Reorder the terms: -400 + 400 + 12r + r2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 12r + r2 = 0 + 400 12r + r2 = 0 + 400 Combine like terms: 0 + 400 = 400 12r + r2 = 400 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = 400 + 36 Reorder the terms: 36 + 12r + r2 = 400 + 36 Combine like terms: 400 + 36 = 436 36 + 12r + r2 = 436 Factor a perfect square on the left side: (r + 6)(r + 6) = 436 Calculate the square root of the right side: 20.880613018 Break this problem into two subproblems by setting (r + 6) equal to 20.880613018 and -20.880613018.Subproblem 1
r + 6 = 20.880613018 Simplifying r + 6 = 20.880613018 Reorder the terms: 6 + r = 20.880613018 Solving 6 + r = 20.880613018 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 20.880613018 + -6 Combine like terms: 6 + -6 = 0 0 + r = 20.880613018 + -6 r = 20.880613018 + -6 Combine like terms: 20.880613018 + -6 = 14.880613018 r = 14.880613018 Simplifying r = 14.880613018Subproblem 2
r + 6 = -20.880613018 Simplifying r + 6 = -20.880613018 Reorder the terms: 6 + r = -20.880613018 Solving 6 + r = -20.880613018 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -20.880613018 + -6 Combine like terms: 6 + -6 = 0 0 + r = -20.880613018 + -6 r = -20.880613018 + -6 Combine like terms: -20.880613018 + -6 = -26.880613018 r = -26.880613018 Simplifying r = -26.880613018Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.880613018, -26.880613018}
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