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Simplifying r2 + -7r + 3 = 0 Reorder the terms: 3 + -7r + r2 = 0 Solving 3 + -7r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -7r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + -7r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7r + r2 = 0 + -3 -7r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7r + r2 = -3 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 = -3 + 12.25 Reorder the terms: 12.25 + -7r + r2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + -7r + r2 = 9.25 Factor a perfect square on the left side: (r + -3.5)(r + -3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (r + -3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
r + -3.5 = 3.041381265 Simplifying r + -3.5 = 3.041381265 Reorder the terms: -3.5 + r = 3.041381265 Solving -3.5 + r = 3.041381265 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 = 3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 3.041381265 + 3.5 r = 3.041381265 + 3.5 Combine like terms: 3.041381265 + 3.5 = 6.541381265 r = 6.541381265 Simplifying r = 6.541381265Subproblem 2
r + -3.5 = -3.041381265 Simplifying r + -3.5 = -3.041381265 Reorder the terms: -3.5 + r = -3.041381265 Solving -3.5 + r = -3.041381265 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 = -3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -3.041381265 + 3.5 r = -3.041381265 + 3.5 Combine like terms: -3.041381265 + 3.5 = 0.458618735 r = 0.458618735 Simplifying r = 0.458618735Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.541381265, 0.458618735}
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