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Simplifying r2 + r + -288 = 0 Reorder the terms: -288 + r + r2 = 0 Solving -288 + r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + r + 288 + r2 = 0 + 288 Reorder the terms: -288 + 288 + r + r2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + r + r2 = 0 + 288 r + r2 = 0 + 288 Combine like terms: 0 + 288 = 288 r + r2 = 288 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. r + 0.25 + r2 = 288 + 0.25 Reorder the terms: 0.25 + r + r2 = 288 + 0.25 Combine like terms: 288 + 0.25 = 288.25 0.25 + r + r2 = 288.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (r + 0.5) equal to 16.977926846 and -16.977926846.Subproblem 1
r + 0.5 = 16.977926846 Simplifying r + 0.5 = 16.977926846 Reorder the terms: 0.5 + r = 16.977926846 Solving 0.5 + r = 16.977926846 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 16.977926846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 16.977926846 + -0.5 r = 16.977926846 + -0.5 Combine like terms: 16.977926846 + -0.5 = 16.477926846 r = 16.477926846 Simplifying r = 16.477926846Subproblem 2
r + 0.5 = -16.977926846 Simplifying r + 0.5 = -16.977926846 Reorder the terms: 0.5 + r = -16.977926846 Solving 0.5 + r = -16.977926846 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -16.977926846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -16.977926846 + -0.5 r = -16.977926846 + -0.5 Combine like terms: -16.977926846 + -0.5 = -17.477926846 r = -17.477926846 Simplifying r = -17.477926846Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.477926846, -17.477926846}
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