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Simplifying 9r2 + -5r + -10 = 10 Reorder the terms: -10 + -5r + 9r2 = 10 Solving -10 + -5r + 9r2 = 10 Solving for variable 'r'. Reorder the terms: -10 + -10 + -5r + 9r2 = 10 + -10 Combine like terms: -10 + -10 = -20 -20 + -5r + 9r2 = 10 + -10 Combine like terms: 10 + -10 = 0 -20 + -5r + 9r2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -0.5555555556r + r2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -0.5555555556r + 2.222222222 + r2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -0.5555555556r + r2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -0.5555555556r + r2 = 0 + 2.222222222 -0.5555555556r + r2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -0.5555555556r + r2 = 2.222222222 The r term is -0.5555555556r. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556r + 0.07716049384 + r2 = 2.222222222 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556r + r2 = 2.222222222 + 0.07716049384 Combine like terms: 2.222222222 + 0.07716049384 = 2.29938271584 0.07716049384 + -0.5555555556r + r2 = 2.29938271584 Factor a perfect square on the left side: (r + -0.2777777778)(r + -0.2777777778) = 2.29938271584 Calculate the square root of the right side: 1.516371563 Break this problem into two subproblems by setting (r + -0.2777777778) equal to 1.516371563 and -1.516371563.Subproblem 1
r + -0.2777777778 = 1.516371563 Simplifying r + -0.2777777778 = 1.516371563 Reorder the terms: -0.2777777778 + r = 1.516371563 Solving -0.2777777778 + r = 1.516371563 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + r = 1.516371563 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + r = 1.516371563 + 0.2777777778 r = 1.516371563 + 0.2777777778 Combine like terms: 1.516371563 + 0.2777777778 = 1.7941493408 r = 1.7941493408 Simplifying r = 1.7941493408Subproblem 2
r + -0.2777777778 = -1.516371563 Simplifying r + -0.2777777778 = -1.516371563 Reorder the terms: -0.2777777778 + r = -1.516371563 Solving -0.2777777778 + r = -1.516371563 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + r = -1.516371563 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + r = -1.516371563 + 0.2777777778 r = -1.516371563 + 0.2777777778 Combine like terms: -1.516371563 + 0.2777777778 = -1.2385937852 r = -1.2385937852 Simplifying r = -1.2385937852Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.7941493408, -1.2385937852}
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