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Simplifying r2 + 7r + -252 = 0 Reorder the terms: -252 + 7r + r2 = 0 Solving -252 + 7r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '252' to each side of the equation. -252 + 7r + 252 + r2 = 0 + 252 Reorder the terms: -252 + 252 + 7r + r2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + 7r + r2 = 0 + 252 7r + r2 = 0 + 252 Combine like terms: 0 + 252 = 252 7r + r2 = 252 The r term is 7r. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7r + 12.25 + r2 = 252 + 12.25 Reorder the terms: 12.25 + 7r + r2 = 252 + 12.25 Combine like terms: 252 + 12.25 = 264.25 12.25 + 7r + r2 = 264.25 Factor a perfect square on the left side: (r + 3.5)(r + 3.5) = 264.25 Calculate the square root of the right side: 16.255768207 Break this problem into two subproblems by setting (r + 3.5) equal to 16.255768207 and -16.255768207.Subproblem 1
r + 3.5 = 16.255768207 Simplifying r + 3.5 = 16.255768207 Reorder the terms: 3.5 + r = 16.255768207 Solving 3.5 + r = 16.255768207 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + r = 16.255768207 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = 16.255768207 + -3.5 r = 16.255768207 + -3.5 Combine like terms: 16.255768207 + -3.5 = 12.755768207 r = 12.755768207 Simplifying r = 12.755768207Subproblem 2
r + 3.5 = -16.255768207 Simplifying r + 3.5 = -16.255768207 Reorder the terms: 3.5 + r = -16.255768207 Solving 3.5 + r = -16.255768207 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + r = -16.255768207 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = -16.255768207 + -3.5 r = -16.255768207 + -3.5 Combine like terms: -16.255768207 + -3.5 = -19.755768207 r = -19.755768207 Simplifying r = -19.755768207Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.755768207, -19.755768207}
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