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Simplifying r2 + 28r + -153.04 = 0 Reorder the terms: -153.04 + 28r + r2 = 0 Solving -153.04 + 28r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '153.04' to each side of the equation. -153.04 + 28r + 153.04 + r2 = 0 + 153.04 Reorder the terms: -153.04 + 153.04 + 28r + r2 = 0 + 153.04 Combine like terms: -153.04 + 153.04 = 0.00 0.00 + 28r + r2 = 0 + 153.04 28r + r2 = 0 + 153.04 Combine like terms: 0 + 153.04 = 153.04 28r + r2 = 153.04 The r term is 28r. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28r + 196 + r2 = 153.04 + 196 Reorder the terms: 196 + 28r + r2 = 153.04 + 196 Combine like terms: 153.04 + 196 = 349.04 196 + 28r + r2 = 349.04 Factor a perfect square on the left side: (r + 14)(r + 14) = 349.04 Calculate the square root of the right side: 18.682612237 Break this problem into two subproblems by setting (r + 14) equal to 18.682612237 and -18.682612237.Subproblem 1
r + 14 = 18.682612237 Simplifying r + 14 = 18.682612237 Reorder the terms: 14 + r = 18.682612237 Solving 14 + r = 18.682612237 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = 18.682612237 + -14 Combine like terms: 14 + -14 = 0 0 + r = 18.682612237 + -14 r = 18.682612237 + -14 Combine like terms: 18.682612237 + -14 = 4.682612237 r = 4.682612237 Simplifying r = 4.682612237Subproblem 2
r + 14 = -18.682612237 Simplifying r + 14 = -18.682612237 Reorder the terms: 14 + r = -18.682612237 Solving 14 + r = -18.682612237 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = -18.682612237 + -14 Combine like terms: 14 + -14 = 0 0 + r = -18.682612237 + -14 r = -18.682612237 + -14 Combine like terms: -18.682612237 + -14 = -32.682612237 r = -32.682612237 Simplifying r = -32.682612237Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.682612237, -32.682612237}
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