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Simplifying r2 + 4r + -5 = 8 Reorder the terms: -5 + 4r + r2 = 8 Solving -5 + 4r + r2 = 8 Solving for variable 'r'. Reorder the terms: -5 + -8 + 4r + r2 = 8 + -8 Combine like terms: -5 + -8 = -13 -13 + 4r + r2 = 8 + -8 Combine like terms: 8 + -8 = 0 -13 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 4r + 13 + r2 = 0 + 13 Reorder the terms: -13 + 13 + 4r + r2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4r + r2 = 0 + 13 4r + r2 = 0 + 13 Combine like terms: 0 + 13 = 13 4r + r2 = 13 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 13 + 4 Reorder the terms: 4 + 4r + r2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + 4r + r2 = 17 Factor a perfect square on the left side: (r + 2)(r + 2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (r + 2) equal to 4.123105626 and -4.123105626.Subproblem 1
r + 2 = 4.123105626 Simplifying r + 2 = 4.123105626 Reorder the terms: 2 + r = 4.123105626 Solving 2 + r = 4.123105626 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + r = 4.123105626 + -2 r = 4.123105626 + -2 Combine like terms: 4.123105626 + -2 = 2.123105626 r = 2.123105626 Simplifying r = 2.123105626Subproblem 2
r + 2 = -4.123105626 Simplifying r + 2 = -4.123105626 Reorder the terms: 2 + r = -4.123105626 Solving 2 + r = -4.123105626 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + r = -4.123105626 + -2 r = -4.123105626 + -2 Combine like terms: -4.123105626 + -2 = -6.123105626 r = -6.123105626 Simplifying r = -6.123105626Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.123105626, -6.123105626}
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