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Simplifying r2 + -4r + -15 = 0 Reorder the terms: -15 + -4r + r2 = 0 Solving -15 + -4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4r + 15 + r2 = 0 + 15 Reorder the terms: -15 + 15 + -4r + r2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4r + r2 = 0 + 15 -4r + r2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4r + r2 = 15 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 15 + 4 Reorder the terms: 4 + -4r + r2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4r + r2 = 19 Factor a perfect square on the left side: (r + -2)(r + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (r + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
r + -2 = 4.358898944 Simplifying r + -2 = 4.358898944 Reorder the terms: -2 + r = 4.358898944 Solving -2 + r = 4.358898944 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + r = 4.358898944 + 2 r = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 r = 6.358898944 Simplifying r = 6.358898944Subproblem 2
r + -2 = -4.358898944 Simplifying r + -2 = -4.358898944 Reorder the terms: -2 + r = -4.358898944 Solving -2 + r = -4.358898944 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + r = -4.358898944 + 2 r = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 r = -2.358898944 Simplifying r = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.358898944, -2.358898944}
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