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Simplifying 10r2 = 17 + 11r Solving 10r2 = 17 + 11r Solving for variable 'r'. Reorder the terms: -17 + -11r + 10r2 = 17 + 11r + -17 + -11r Reorder the terms: -17 + -11r + 10r2 = 17 + -17 + 11r + -11r Combine like terms: 17 + -17 = 0 -17 + -11r + 10r2 = 0 + 11r + -11r -17 + -11r + 10r2 = 11r + -11r Combine like terms: 11r + -11r = 0 -17 + -11r + 10r2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.7 + -1.1r + r2 = 0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + -1.1r + 1.7 + r2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + -1.1r + r2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + -1.1r + r2 = 0 + 1.7 -1.1r + r2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 -1.1r + r2 = 1.7 The r term is -1.1r. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1r + 0.3025 + r2 = 1.7 + 0.3025 Reorder the terms: 0.3025 + -1.1r + r2 = 1.7 + 0.3025 Combine like terms: 1.7 + 0.3025 = 2.0025 0.3025 + -1.1r + r2 = 2.0025 Factor a perfect square on the left side: (r + -0.55)(r + -0.55) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (r + -0.55) equal to 1.41509717 and -1.41509717.Subproblem 1
r + -0.55 = 1.41509717 Simplifying r + -0.55 = 1.41509717 Reorder the terms: -0.55 + r = 1.41509717 Solving -0.55 + r = 1.41509717 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + r = 1.41509717 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + r = 1.41509717 + 0.55 r = 1.41509717 + 0.55 Combine like terms: 1.41509717 + 0.55 = 1.96509717 r = 1.96509717 Simplifying r = 1.96509717Subproblem 2
r + -0.55 = -1.41509717 Simplifying r + -0.55 = -1.41509717 Reorder the terms: -0.55 + r = -1.41509717 Solving -0.55 + r = -1.41509717 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + r = -1.41509717 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + r = -1.41509717 + 0.55 r = -1.41509717 + 0.55 Combine like terms: -1.41509717 + 0.55 = -0.86509717 r = -0.86509717 Simplifying r = -0.86509717Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.96509717, -0.86509717}
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