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Simplifying 9r2 + -14 = -10r Reorder the terms: -14 + 9r2 = -10r Solving -14 + 9r2 = -10r Solving for variable 'r'. Reorder the terms: -14 + 10r + 9r2 = -10r + 10r Combine like terms: -10r + 10r = 0 -14 + 10r + 9r2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 1.111111111r + r2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 1.111111111r + 1.555555556 + r2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 1.111111111r + r2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 1.111111111r + r2 = 0 + 1.555555556 1.111111111r + r2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 1.111111111r + r2 = 1.555555556 The r term is 1.111111111r. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111r + 0.3086419752 + r2 = 1.555555556 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111r + r2 = 1.555555556 + 0.3086419752 Combine like terms: 1.555555556 + 0.3086419752 = 1.8641975312 0.3086419752 + 1.111111111r + r2 = 1.8641975312 Factor a perfect square on the left side: (r + 0.5555555555)(r + 0.5555555555) = 1.8641975312 Calculate the square root of the right side: 1.365356192 Break this problem into two subproblems by setting (r + 0.5555555555) equal to 1.365356192 and -1.365356192.Subproblem 1
r + 0.5555555555 = 1.365356192 Simplifying r + 0.5555555555 = 1.365356192 Reorder the terms: 0.5555555555 + r = 1.365356192 Solving 0.5555555555 + r = 1.365356192 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + r = 1.365356192 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + r = 1.365356192 + -0.5555555555 r = 1.365356192 + -0.5555555555 Combine like terms: 1.365356192 + -0.5555555555 = 0.8098006365 r = 0.8098006365 Simplifying r = 0.8098006365Subproblem 2
r + 0.5555555555 = -1.365356192 Simplifying r + 0.5555555555 = -1.365356192 Reorder the terms: 0.5555555555 + r = -1.365356192 Solving 0.5555555555 + r = -1.365356192 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + r = -1.365356192 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + r = -1.365356192 + -0.5555555555 r = -1.365356192 + -0.5555555555 Combine like terms: -1.365356192 + -0.5555555555 = -1.9209117475 r = -1.9209117475 Simplifying r = -1.9209117475Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.8098006365, -1.9209117475}
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