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Simplifying r2 + 10r + -25 = 0 Reorder the terms: -25 + 10r + r2 = 0 Solving -25 + 10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 10r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + 10r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 10r + r2 = 0 + 25 10r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 10r + r2 = 25 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 = 25 + 25 Reorder the terms: 25 + 10r + r2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + 10r + r2 = 50 Factor a perfect square on the left side: (r + 5)(r + 5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (r + 5) equal to 7.071067812 and -7.071067812.Subproblem 1
r + 5 = 7.071067812 Simplifying r + 5 = 7.071067812 Reorder the terms: 5 + r = 7.071067812 Solving 5 + r = 7.071067812 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 = 7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + r = 7.071067812 + -5 r = 7.071067812 + -5 Combine like terms: 7.071067812 + -5 = 2.071067812 r = 2.071067812 Simplifying r = 2.071067812Subproblem 2
r + 5 = -7.071067812 Simplifying r + 5 = -7.071067812 Reorder the terms: 5 + r = -7.071067812 Solving 5 + r = -7.071067812 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 = -7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + r = -7.071067812 + -5 r = -7.071067812 + -5 Combine like terms: -7.071067812 + -5 = -12.071067812 r = -12.071067812 Simplifying r = -12.071067812Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.071067812, -12.071067812}
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