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Simplifying r2 + 14r + -42 = 0 Reorder the terms: -42 + 14r + r2 = 0 Solving -42 + 14r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 14r + 42 + r2 = 0 + 42 Reorder the terms: -42 + 42 + 14r + r2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 14r + r2 = 0 + 42 14r + r2 = 0 + 42 Combine like terms: 0 + 42 = 42 14r + r2 = 42 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 = 42 + 49 Reorder the terms: 49 + 14r + r2 = 42 + 49 Combine like terms: 42 + 49 = 91 49 + 14r + r2 = 91 Factor a perfect square on the left side: (r + 7)(r + 7) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (r + 7) equal to 9.539392014 and -9.539392014.Subproblem 1
r + 7 = 9.539392014 Simplifying r + 7 = 9.539392014 Reorder the terms: 7 + r = 9.539392014 Solving 7 + r = 9.539392014 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 = 9.539392014 + -7 Combine like terms: 7 + -7 = 0 0 + r = 9.539392014 + -7 r = 9.539392014 + -7 Combine like terms: 9.539392014 + -7 = 2.539392014 r = 2.539392014 Simplifying r = 2.539392014Subproblem 2
r + 7 = -9.539392014 Simplifying r + 7 = -9.539392014 Reorder the terms: 7 + r = -9.539392014 Solving 7 + r = -9.539392014 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 = -9.539392014 + -7 Combine like terms: 7 + -7 = 0 0 + r = -9.539392014 + -7 r = -9.539392014 + -7 Combine like terms: -9.539392014 + -7 = -16.539392014 r = -16.539392014 Simplifying r = -16.539392014Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.539392014, -16.539392014}
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