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Simplifying r2 + -12r = 25 Reorder the terms: -12r + r2 = 25 Solving -12r + r2 = 25 Solving for variable 'r'. Reorder the terms: -25 + -12r + r2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -12r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -12r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + -12r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -12r + r2 = 0 + 25 -12r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 -12r + r2 = 25 The r term is -12r. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12r + 36 + r2 = 25 + 36 Reorder the terms: 36 + -12r + r2 = 25 + 36 Combine like terms: 25 + 36 = 61 36 + -12r + r2 = 61 Factor a perfect square on the left side: (r + -6)(r + -6) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (r + -6) equal to 7.810249676 and -7.810249676.Subproblem 1
r + -6 = 7.810249676 Simplifying r + -6 = 7.810249676 Reorder the terms: -6 + r = 7.810249676 Solving -6 + r = 7.810249676 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 7.810249676 + 6 Combine like terms: -6 + 6 = 0 0 + r = 7.810249676 + 6 r = 7.810249676 + 6 Combine like terms: 7.810249676 + 6 = 13.810249676 r = 13.810249676 Simplifying r = 13.810249676Subproblem 2
r + -6 = -7.810249676 Simplifying r + -6 = -7.810249676 Reorder the terms: -6 + r = -7.810249676 Solving -6 + r = -7.810249676 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -7.810249676 + 6 Combine like terms: -6 + 6 = 0 0 + r = -7.810249676 + 6 r = -7.810249676 + 6 Combine like terms: -7.810249676 + 6 = -1.810249676 r = -1.810249676 Simplifying r = -1.810249676Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.810249676, -1.810249676}
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