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Simplifying r2 + -10r + -32 = 0 Reorder the terms: -32 + -10r + r2 = 0 Solving -32 + -10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -10r + 32 + r2 = 0 + 32 Reorder the terms: -32 + 32 + -10r + r2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -10r + r2 = 0 + 32 -10r + r2 = 0 + 32 Combine like terms: 0 + 32 = 32 -10r + r2 = 32 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = 32 + 25 Reorder the terms: 25 + -10r + r2 = 32 + 25 Combine like terms: 32 + 25 = 57 25 + -10r + r2 = 57 Factor a perfect square on the left side: (r + -5)(r + -5) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (r + -5) equal to 7.549834435 and -7.549834435.Subproblem 1
r + -5 = 7.549834435 Simplifying r + -5 = 7.549834435 Reorder the terms: -5 + r = 7.549834435 Solving -5 + r = 7.549834435 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 7.549834435 + 5 Combine like terms: -5 + 5 = 0 0 + r = 7.549834435 + 5 r = 7.549834435 + 5 Combine like terms: 7.549834435 + 5 = 12.549834435 r = 12.549834435 Simplifying r = 12.549834435Subproblem 2
r + -5 = -7.549834435 Simplifying r + -5 = -7.549834435 Reorder the terms: -5 + r = -7.549834435 Solving -5 + r = -7.549834435 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -7.549834435 + 5 Combine like terms: -5 + 5 = 0 0 + r = -7.549834435 + 5 r = -7.549834435 + 5 Combine like terms: -7.549834435 + 5 = -2.549834435 r = -2.549834435 Simplifying r = -2.549834435Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.549834435, -2.549834435}
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