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Simplifying r2 + -6r + -10 = -7 Reorder the terms: -10 + -6r + r2 = -7 Solving -10 + -6r + r2 = -7 Solving for variable 'r'. Reorder the terms: -10 + 7 + -6r + r2 = -7 + 7 Combine like terms: -10 + 7 = -3 -3 + -6r + r2 = -7 + 7 Combine like terms: -7 + 7 = 0 -3 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + -6r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6r + r2 = 0 + 3 -6r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6r + r2 = 3 The r term is -6r. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6r + 9 + r2 = 3 + 9 Reorder the terms: 9 + -6r + r2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6r + r2 = 12 Factor a perfect square on the left side: (r + -3)(r + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (r + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
r + -3 = 3.464101615 Simplifying r + -3 = 3.464101615 Reorder the terms: -3 + r = 3.464101615 Solving -3 + r = 3.464101615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + r = 3.464101615 + 3 r = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 r = 6.464101615 Simplifying r = 6.464101615Subproblem 2
r + -3 = -3.464101615 Simplifying r + -3 = -3.464101615 Reorder the terms: -3 + r = -3.464101615 Solving -3 + r = -3.464101615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + r = -3.464101615 + 3 r = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 r = -0.464101615 Simplifying r = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.464101615, -0.464101615}
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