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Simplifying r2 + 7r + -342 = 0 Reorder the terms: -342 + 7r + r2 = 0 Solving -342 + 7r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '342' to each side of the equation. -342 + 7r + 342 + r2 = 0 + 342 Reorder the terms: -342 + 342 + 7r + r2 = 0 + 342 Combine like terms: -342 + 342 = 0 0 + 7r + r2 = 0 + 342 7r + r2 = 0 + 342 Combine like terms: 0 + 342 = 342 7r + r2 = 342 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 = 342 + 12.25 Reorder the terms: 12.25 + 7r + r2 = 342 + 12.25 Combine like terms: 342 + 12.25 = 354.25 12.25 + 7r + r2 = 354.25 Factor a perfect square on the left side: (r + 3.5)(r + 3.5) = 354.25 Calculate the square root of the right side: 18.821530225 Break this problem into two subproblems by setting (r + 3.5) equal to 18.821530225 and -18.821530225.Subproblem 1
r + 3.5 = 18.821530225 Simplifying r + 3.5 = 18.821530225 Reorder the terms: 3.5 + r = 18.821530225 Solving 3.5 + r = 18.821530225 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 = 18.821530225 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = 18.821530225 + -3.5 r = 18.821530225 + -3.5 Combine like terms: 18.821530225 + -3.5 = 15.321530225 r = 15.321530225 Simplifying r = 15.321530225Subproblem 2
r + 3.5 = -18.821530225 Simplifying r + 3.5 = -18.821530225 Reorder the terms: 3.5 + r = -18.821530225 Solving 3.5 + r = -18.821530225 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 = -18.821530225 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = -18.821530225 + -3.5 r = -18.821530225 + -3.5 Combine like terms: -18.821530225 + -3.5 = -22.321530225 r = -22.321530225 Simplifying r = -22.321530225Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.321530225, -22.321530225}
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