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Simplifying r2 + -10r + -750 = 0 Reorder the terms: -750 + -10r + r2 = 0 Solving -750 + -10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + -10r + 750 + r2 = 0 + 750 Reorder the terms: -750 + 750 + -10r + r2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -10r + r2 = 0 + 750 -10r + r2 = 0 + 750 Combine like terms: 0 + 750 = 750 -10r + r2 = 750 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 = 750 + 25 Reorder the terms: 25 + -10r + r2 = 750 + 25 Combine like terms: 750 + 25 = 775 25 + -10r + r2 = 775 Factor a perfect square on the left side: (r + -5)(r + -5) = 775 Calculate the square root of the right side: 27.838821814 Break this problem into two subproblems by setting (r + -5) equal to 27.838821814 and -27.838821814.Subproblem 1
r + -5 = 27.838821814 Simplifying r + -5 = 27.838821814 Reorder the terms: -5 + r = 27.838821814 Solving -5 + r = 27.838821814 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 = 27.838821814 + 5 Combine like terms: -5 + 5 = 0 0 + r = 27.838821814 + 5 r = 27.838821814 + 5 Combine like terms: 27.838821814 + 5 = 32.838821814 r = 32.838821814 Simplifying r = 32.838821814Subproblem 2
r + -5 = -27.838821814 Simplifying r + -5 = -27.838821814 Reorder the terms: -5 + r = -27.838821814 Solving -5 + r = -27.838821814 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 = -27.838821814 + 5 Combine like terms: -5 + 5 = 0 0 + r = -27.838821814 + 5 r = -27.838821814 + 5 Combine like terms: -27.838821814 + 5 = -22.838821814 r = -22.838821814 Simplifying r = -22.838821814Solution
The solution to the problem is based on the solutions from the subproblems. r = {32.838821814, -22.838821814}
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