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Simplifying r2 + 2r + -90 = -6 Reorder the terms: -90 + 2r + r2 = -6 Solving -90 + 2r + r2 = -6 Solving for variable 'r'. Reorder the terms: -90 + 6 + 2r + r2 = -6 + 6 Combine like terms: -90 + 6 = -84 -84 + 2r + r2 = -6 + 6 Combine like terms: -6 + 6 = 0 -84 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 2r + 84 + r2 = 0 + 84 Reorder the terms: -84 + 84 + 2r + r2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 2r + r2 = 0 + 84 2r + r2 = 0 + 84 Combine like terms: 0 + 84 = 84 2r + r2 = 84 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 = 84 + 1 Reorder the terms: 1 + 2r + r2 = 84 + 1 Combine like terms: 84 + 1 = 85 1 + 2r + r2 = 85 Factor a perfect square on the left side: (r + 1)(r + 1) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (r + 1) equal to 9.219544457 and -9.219544457.Subproblem 1
r + 1 = 9.219544457 Simplifying r + 1 = 9.219544457 Reorder the terms: 1 + r = 9.219544457 Solving 1 + r = 9.219544457 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 = 9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + r = 9.219544457 + -1 r = 9.219544457 + -1 Combine like terms: 9.219544457 + -1 = 8.219544457 r = 8.219544457 Simplifying r = 8.219544457Subproblem 2
r + 1 = -9.219544457 Simplifying r + 1 = -9.219544457 Reorder the terms: 1 + r = -9.219544457 Solving 1 + r = -9.219544457 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 = -9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + r = -9.219544457 + -1 r = -9.219544457 + -1 Combine like terms: -9.219544457 + -1 = -10.219544457 r = -10.219544457 Simplifying r = -10.219544457Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.219544457, -10.219544457}
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