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Simplifying r2 + -20r + -67 = 7 Reorder the terms: -67 + -20r + r2 = 7 Solving -67 + -20r + r2 = 7 Solving for variable 'r'. Reorder the terms: -67 + -7 + -20r + r2 = 7 + -7 Combine like terms: -67 + -7 = -74 -74 + -20r + r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -74 + -20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -20r + 74 + r2 = 0 + 74 Reorder the terms: -74 + 74 + -20r + r2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -20r + r2 = 0 + 74 -20r + r2 = 0 + 74 Combine like terms: 0 + 74 = 74 -20r + r2 = 74 The r term is -20r. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20r + 100 + r2 = 74 + 100 Reorder the terms: 100 + -20r + r2 = 74 + 100 Combine like terms: 74 + 100 = 174 100 + -20r + r2 = 174 Factor a perfect square on the left side: (r + -10)(r + -10) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (r + -10) equal to 13.190905958 and -13.190905958.Subproblem 1
r + -10 = 13.190905958 Simplifying r + -10 = 13.190905958 Reorder the terms: -10 + r = 13.190905958 Solving -10 + r = 13.190905958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 13.190905958 + 10 Combine like terms: -10 + 10 = 0 0 + r = 13.190905958 + 10 r = 13.190905958 + 10 Combine like terms: 13.190905958 + 10 = 23.190905958 r = 23.190905958 Simplifying r = 23.190905958Subproblem 2
r + -10 = -13.190905958 Simplifying r + -10 = -13.190905958 Reorder the terms: -10 + r = -13.190905958 Solving -10 + r = -13.190905958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -13.190905958 + 10 Combine like terms: -10 + 10 = 0 0 + r = -13.190905958 + 10 r = -13.190905958 + 10 Combine like terms: -13.190905958 + 10 = -3.190905958 r = -3.190905958 Simplifying r = -3.190905958Solution
The solution to the problem is based on the solutions from the subproblems. r = {23.190905958, -3.190905958}
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