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Simplifying r2 + -2r = 90 Reorder the terms: -2r + r2 = 90 Solving -2r + r2 = 90 Solving for variable 'r'. Reorder the terms: -90 + -2r + r2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -2r + 90 + r2 = 0 + 90 Reorder the terms: -90 + 90 + -2r + r2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -2r + r2 = 0 + 90 -2r + r2 = 0 + 90 Combine like terms: 0 + 90 = 90 -2r + r2 = 90 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 = 90 + 1 Reorder the terms: 1 + -2r + r2 = 90 + 1 Combine like terms: 90 + 1 = 91 1 + -2r + r2 = 91 Factor a perfect square on the left side: (r + -1)(r + -1) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (r + -1) equal to 9.539392014 and -9.539392014.Subproblem 1
r + -1 = 9.539392014 Simplifying r + -1 = 9.539392014 Reorder the terms: -1 + r = 9.539392014 Solving -1 + r = 9.539392014 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 = 9.539392014 + 1 Combine like terms: -1 + 1 = 0 0 + r = 9.539392014 + 1 r = 9.539392014 + 1 Combine like terms: 9.539392014 + 1 = 10.539392014 r = 10.539392014 Simplifying r = 10.539392014Subproblem 2
r + -1 = -9.539392014 Simplifying r + -1 = -9.539392014 Reorder the terms: -1 + r = -9.539392014 Solving -1 + r = -9.539392014 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 = -9.539392014 + 1 Combine like terms: -1 + 1 = 0 0 + r = -9.539392014 + 1 r = -9.539392014 + 1 Combine like terms: -9.539392014 + 1 = -8.539392014 r = -8.539392014 Simplifying r = -8.539392014Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.539392014, -8.539392014}
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