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Simplifying r2 + -16r + 21 = 4 Reorder the terms: 21 + -16r + r2 = 4 Solving 21 + -16r + r2 = 4 Solving for variable 'r'. Reorder the terms: 21 + -4 + -16r + r2 = 4 + -4 Combine like terms: 21 + -4 = 17 17 + -16r + r2 = 4 + -4 Combine like terms: 4 + -4 = 0 17 + -16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -16r + -17 + r2 = 0 + -17 Reorder the terms: 17 + -17 + -16r + r2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -16r + r2 = 0 + -17 -16r + r2 = 0 + -17 Combine like terms: 0 + -17 = -17 -16r + r2 = -17 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 = -17 + 64 Reorder the terms: 64 + -16r + r2 = -17 + 64 Combine like terms: -17 + 64 = 47 64 + -16r + r2 = 47 Factor a perfect square on the left side: (r + -8)(r + -8) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (r + -8) equal to 6.8556546 and -6.8556546.Subproblem 1
r + -8 = 6.8556546 Simplifying r + -8 = 6.8556546 Reorder the terms: -8 + r = 6.8556546 Solving -8 + r = 6.8556546 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 = 6.8556546 + 8 Combine like terms: -8 + 8 = 0 0 + r = 6.8556546 + 8 r = 6.8556546 + 8 Combine like terms: 6.8556546 + 8 = 14.8556546 r = 14.8556546 Simplifying r = 14.8556546Subproblem 2
r + -8 = -6.8556546 Simplifying r + -8 = -6.8556546 Reorder the terms: -8 + r = -6.8556546 Solving -8 + r = -6.8556546 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 = -6.8556546 + 8 Combine like terms: -8 + 8 = 0 0 + r = -6.8556546 + 8 r = -6.8556546 + 8 Combine like terms: -6.8556546 + 8 = 1.1443454 r = 1.1443454 Simplifying r = 1.1443454Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.8556546, 1.1443454}
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