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Simplifying r2 + 16r + -63 = 4 Reorder the terms: -63 + 16r + r2 = 4 Solving -63 + 16r + r2 = 4 Solving for variable 'r'. Reorder the terms: -63 + -4 + 16r + r2 = 4 + -4 Combine like terms: -63 + -4 = -67 -67 + 16r + r2 = 4 + -4 Combine like terms: 4 + -4 = 0 -67 + 16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 16r + 67 + r2 = 0 + 67 Reorder the terms: -67 + 67 + 16r + r2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 16r + r2 = 0 + 67 16r + r2 = 0 + 67 Combine like terms: 0 + 67 = 67 16r + r2 = 67 The r term is 16r. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16r + 64 + r2 = 67 + 64 Reorder the terms: 64 + 16r + r2 = 67 + 64 Combine like terms: 67 + 64 = 131 64 + 16r + r2 = 131 Factor a perfect square on the left side: (r + 8)(r + 8) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (r + 8) equal to 11.445523142 and -11.445523142.Subproblem 1
r + 8 = 11.445523142 Simplifying r + 8 = 11.445523142 Reorder the terms: 8 + r = 11.445523142 Solving 8 + r = 11.445523142 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 11.445523142 + -8 Combine like terms: 8 + -8 = 0 0 + r = 11.445523142 + -8 r = 11.445523142 + -8 Combine like terms: 11.445523142 + -8 = 3.445523142 r = 3.445523142 Simplifying r = 3.445523142Subproblem 2
r + 8 = -11.445523142 Simplifying r + 8 = -11.445523142 Reorder the terms: 8 + r = -11.445523142 Solving 8 + r = -11.445523142 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -11.445523142 + -8 Combine like terms: 8 + -8 = 0 0 + r = -11.445523142 + -8 r = -11.445523142 + -8 Combine like terms: -11.445523142 + -8 = -19.445523142 r = -19.445523142 Simplifying r = -19.445523142Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.445523142, -19.445523142}
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