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Simplifying 6.24r2 + 87.36r + -6 = 0 Reorder the terms: -6 + 87.36r + 6.24r2 = 0 Solving -6 + 87.36r + 6.24r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 6.24 the coefficient of the squared term: Divide each side by '6.24'. -0.9615384615 + 14r + r2 = 0 Move the constant term to the right: Add '0.9615384615' to each side of the equation. -0.9615384615 + 14r + 0.9615384615 + r2 = 0 + 0.9615384615 Reorder the terms: -0.9615384615 + 0.9615384615 + 14r + r2 = 0 + 0.9615384615 Combine like terms: -0.9615384615 + 0.9615384615 = 0.0000000000 0.0000000000 + 14r + r2 = 0 + 0.9615384615 14r + r2 = 0 + 0.9615384615 Combine like terms: 0 + 0.9615384615 = 0.9615384615 14r + r2 = 0.9615384615 The r term is 14r. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14r + 49 + r2 = 0.9615384615 + 49 Reorder the terms: 49 + 14r + r2 = 0.9615384615 + 49 Combine like terms: 0.9615384615 + 49 = 49.9615384615 49 + 14r + r2 = 49.9615384615 Factor a perfect square on the left side: (r + 7)(r + 7) = 49.9615384615 Calculate the square root of the right side: 7.068347647 Break this problem into two subproblems by setting (r + 7) equal to 7.068347647 and -7.068347647.Subproblem 1
r + 7 = 7.068347647 Simplifying r + 7 = 7.068347647 Reorder the terms: 7 + r = 7.068347647 Solving 7 + r = 7.068347647 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 7.068347647 + -7 Combine like terms: 7 + -7 = 0 0 + r = 7.068347647 + -7 r = 7.068347647 + -7 Combine like terms: 7.068347647 + -7 = 0.068347647 r = 0.068347647 Simplifying r = 0.068347647Subproblem 2
r + 7 = -7.068347647 Simplifying r + 7 = -7.068347647 Reorder the terms: 7 + r = -7.068347647 Solving 7 + r = -7.068347647 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -7.068347647 + -7 Combine like terms: 7 + -7 = 0 0 + r = -7.068347647 + -7 r = -7.068347647 + -7 Combine like terms: -7.068347647 + -7 = -14.068347647 r = -14.068347647 Simplifying r = -14.068347647Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.068347647, -14.068347647}
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