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Simplifying r2 + 2r + 5 = 10 Reorder the terms: 5 + 2r + r2 = 10 Solving 5 + 2r + r2 = 10 Solving for variable 'r'. Reorder the terms: 5 + -10 + 2r + r2 = 10 + -10 Combine like terms: 5 + -10 = -5 -5 + 2r + r2 = 10 + -10 Combine like terms: 10 + -10 = 0 -5 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2r + 5 + r2 = 0 + 5 Reorder the terms: -5 + 5 + 2r + r2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2r + r2 = 0 + 5 2r + r2 = 0 + 5 Combine like terms: 0 + 5 = 5 2r + r2 = 5 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 5 + 1 Reorder the terms: 1 + 2r + r2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2r + r2 = 6 Factor a perfect square on the left side: (r + 1)(r + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (r + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
r + 1 = 2.449489743 Simplifying r + 1 = 2.449489743 Reorder the terms: 1 + r = 2.449489743 Solving 1 + r = 2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + r = 2.449489743 + -1 r = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 r = 1.449489743 Simplifying r = 1.449489743Subproblem 2
r + 1 = -2.449489743 Simplifying r + 1 = -2.449489743 Reorder the terms: 1 + r = -2.449489743 Solving 1 + r = -2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + r = -2.449489743 + -1 r = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 r = -3.449489743 Simplifying r = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.449489743, -3.449489743}
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