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Simplifying 5r2 + -44 + -30 = 11r Reorder the terms: -44 + -30 + 5r2 = 11r Combine like terms: -44 + -30 = -74 -74 + 5r2 = 11r Solving -74 + 5r2 = 11r Solving for variable 'r'. Reorder the terms: -74 + -11r + 5r2 = 11r + -11r Combine like terms: 11r + -11r = 0 -74 + -11r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.8 + -2.2r + r2 = 0 Move the constant term to the right: Add '14.8' to each side of the equation. -14.8 + -2.2r + 14.8 + r2 = 0 + 14.8 Reorder the terms: -14.8 + 14.8 + -2.2r + r2 = 0 + 14.8 Combine like terms: -14.8 + 14.8 = 0.0 0.0 + -2.2r + r2 = 0 + 14.8 -2.2r + r2 = 0 + 14.8 Combine like terms: 0 + 14.8 = 14.8 -2.2r + r2 = 14.8 The r term is -2.2r. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2r + 1.21 + r2 = 14.8 + 1.21 Reorder the terms: 1.21 + -2.2r + r2 = 14.8 + 1.21 Combine like terms: 14.8 + 1.21 = 16.01 1.21 + -2.2r + r2 = 16.01 Factor a perfect square on the left side: (r + -1.1)(r + -1.1) = 16.01 Calculate the square root of the right side: 4.001249805 Break this problem into two subproblems by setting (r + -1.1) equal to 4.001249805 and -4.001249805.Subproblem 1
r + -1.1 = 4.001249805 Simplifying r + -1.1 = 4.001249805 Reorder the terms: -1.1 + r = 4.001249805 Solving -1.1 + r = 4.001249805 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + r = 4.001249805 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + r = 4.001249805 + 1.1 r = 4.001249805 + 1.1 Combine like terms: 4.001249805 + 1.1 = 5.101249805 r = 5.101249805 Simplifying r = 5.101249805Subproblem 2
r + -1.1 = -4.001249805 Simplifying r + -1.1 = -4.001249805 Reorder the terms: -1.1 + r = -4.001249805 Solving -1.1 + r = -4.001249805 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + r = -4.001249805 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + r = -4.001249805 + 1.1 r = -4.001249805 + 1.1 Combine like terms: -4.001249805 + 1.1 = -2.901249805 r = -2.901249805 Simplifying r = -2.901249805Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.101249805, -2.901249805}
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