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Simplifying r2 + -20r + -36 = 4 Reorder the terms: -36 + -20r + r2 = 4 Solving -36 + -20r + r2 = 4 Solving for variable 'r'. Reorder the terms: -36 + -4 + -20r + r2 = 4 + -4 Combine like terms: -36 + -4 = -40 -40 + -20r + r2 = 4 + -4 Combine like terms: 4 + -4 = 0 -40 + -20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -20r + 40 + r2 = 0 + 40 Reorder the terms: -40 + 40 + -20r + r2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -20r + r2 = 0 + 40 -20r + r2 = 0 + 40 Combine like terms: 0 + 40 = 40 -20r + r2 = 40 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 = 40 + 100 Reorder the terms: 100 + -20r + r2 = 40 + 100 Combine like terms: 40 + 100 = 140 100 + -20r + r2 = 140 Factor a perfect square on the left side: (r + -10)(r + -10) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (r + -10) equal to 11.832159566 and -11.832159566.Subproblem 1
r + -10 = 11.832159566 Simplifying r + -10 = 11.832159566 Reorder the terms: -10 + r = 11.832159566 Solving -10 + r = 11.832159566 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 = 11.832159566 + 10 Combine like terms: -10 + 10 = 0 0 + r = 11.832159566 + 10 r = 11.832159566 + 10 Combine like terms: 11.832159566 + 10 = 21.832159566 r = 21.832159566 Simplifying r = 21.832159566Subproblem 2
r + -10 = -11.832159566 Simplifying r + -10 = -11.832159566 Reorder the terms: -10 + r = -11.832159566 Solving -10 + r = -11.832159566 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 = -11.832159566 + 10 Combine like terms: -10 + 10 = 0 0 + r = -11.832159566 + 10 r = -11.832159566 + 10 Combine like terms: -11.832159566 + 10 = -1.832159566 r = -1.832159566 Simplifying r = -1.832159566Solution
The solution to the problem is based on the solutions from the subproblems. r = {21.832159566, -1.832159566}
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