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Simplifying r(r + 14) = 2 Reorder the terms: r(14 + r) = 2 (14 * r + r * r) = 2 (14r + r2) = 2 Solving 14r + r2 = 2 Solving for variable 'r'. Reorder the terms: -2 + 14r + r2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 14r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + 14r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 14r + r2 = 0 + 2 14r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 14r + r2 = 2 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 = 2 + 49 Reorder the terms: 49 + 14r + r2 = 2 + 49 Combine like terms: 2 + 49 = 51 49 + 14r + r2 = 51 Factor a perfect square on the left side: (r + 7)(r + 7) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (r + 7) equal to 7.141428429 and -7.141428429.Subproblem 1
r + 7 = 7.141428429 Simplifying r + 7 = 7.141428429 Reorder the terms: 7 + r = 7.141428429 Solving 7 + r = 7.141428429 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 = 7.141428429 + -7 Combine like terms: 7 + -7 = 0 0 + r = 7.141428429 + -7 r = 7.141428429 + -7 Combine like terms: 7.141428429 + -7 = 0.141428429 r = 0.141428429 Simplifying r = 0.141428429Subproblem 2
r + 7 = -7.141428429 Simplifying r + 7 = -7.141428429 Reorder the terms: 7 + r = -7.141428429 Solving 7 + r = -7.141428429 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 = -7.141428429 + -7 Combine like terms: 7 + -7 = 0 0 + r = -7.141428429 + -7 r = -7.141428429 + -7 Combine like terms: -7.141428429 + -7 = -14.141428429 r = -14.141428429 Simplifying r = -14.141428429Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.141428429, -14.141428429}
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