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Simplifying 0 = r2 + 15.6r + -135.31 Reorder the terms: 0 = -135.31 + 15.6r + r2 Solving 0 = -135.31 + 15.6r + r2 Solving for variable 'r'. Combine like terms: 0 + 135.31 = 135.31 135.31 + -15.6r + -1r2 = -135.31 + 15.6r + r2 + 135.31 + -15.6r + -1r2 Reorder the terms: 135.31 + -15.6r + -1r2 = -135.31 + 135.31 + 15.6r + -15.6r + r2 + -1r2 Combine like terms: -135.31 + 135.31 = 0.00 135.31 + -15.6r + -1r2 = 0.00 + 15.6r + -15.6r + r2 + -1r2 135.31 + -15.6r + -1r2 = 15.6r + -15.6r + r2 + -1r2 Combine like terms: 15.6r + -15.6r = 0.0 135.31 + -15.6r + -1r2 = 0.0 + r2 + -1r2 135.31 + -15.6r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 135.31 + -15.6r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -135.31 + 15.6r + r2 = 0 Move the constant term to the right: Add '135.31' to each side of the equation. -135.31 + 15.6r + 135.31 + r2 = 0 + 135.31 Reorder the terms: -135.31 + 135.31 + 15.6r + r2 = 0 + 135.31 Combine like terms: -135.31 + 135.31 = 0.00 0.00 + 15.6r + r2 = 0 + 135.31 15.6r + r2 = 0 + 135.31 Combine like terms: 0 + 135.31 = 135.31 15.6r + r2 = 135.31 The r term is 15.6r. Take half its coefficient (7.8). Square it (60.84) and add it to both sides. Add '60.84' to each side of the equation. 15.6r + 60.84 + r2 = 135.31 + 60.84 Reorder the terms: 60.84 + 15.6r + r2 = 135.31 + 60.84 Combine like terms: 135.31 + 60.84 = 196.15 60.84 + 15.6r + r2 = 196.15 Factor a perfect square on the left side: (r + 7.8)(r + 7.8) = 196.15 Calculate the square root of the right side: 14.005356118 Break this problem into two subproblems by setting (r + 7.8) equal to 14.005356118 and -14.005356118.Subproblem 1
r + 7.8 = 14.005356118 Simplifying r + 7.8 = 14.005356118 Reorder the terms: 7.8 + r = 14.005356118 Solving 7.8 + r = 14.005356118 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + r = 14.005356118 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + r = 14.005356118 + -7.8 r = 14.005356118 + -7.8 Combine like terms: 14.005356118 + -7.8 = 6.205356118 r = 6.205356118 Simplifying r = 6.205356118Subproblem 2
r + 7.8 = -14.005356118 Simplifying r + 7.8 = -14.005356118 Reorder the terms: 7.8 + r = -14.005356118 Solving 7.8 + r = -14.005356118 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + r = -14.005356118 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + r = -14.005356118 + -7.8 r = -14.005356118 + -7.8 Combine like terms: -14.005356118 + -7.8 = -21.805356118 r = -21.805356118 Simplifying r = -21.805356118Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.205356118, -21.805356118}
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