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Simplifying 10r2 + -19r + 8 = 0 Reorder the terms: 8 + -19r + 10r2 = 0 Solving 8 + -19r + 10r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.8 + -1.9r + r2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -1.9r + -0.8 + r2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -1.9r + r2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -1.9r + r2 = 0 + -0.8 -1.9r + r2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -1.9r + r2 = -0.8 The r term is -1.9r. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9r + 0.9025 + r2 = -0.8 + 0.9025 Reorder the terms: 0.9025 + -1.9r + r2 = -0.8 + 0.9025 Combine like terms: -0.8 + 0.9025 = 0.1025 0.9025 + -1.9r + r2 = 0.1025 Factor a perfect square on the left side: (r + -0.95)(r + -0.95) = 0.1025 Calculate the square root of the right side: 0.320156212 Break this problem into two subproblems by setting (r + -0.95) equal to 0.320156212 and -0.320156212.Subproblem 1
r + -0.95 = 0.320156212 Simplifying r + -0.95 = 0.320156212 Reorder the terms: -0.95 + r = 0.320156212 Solving -0.95 + r = 0.320156212 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + r = 0.320156212 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + r = 0.320156212 + 0.95 r = 0.320156212 + 0.95 Combine like terms: 0.320156212 + 0.95 = 1.270156212 r = 1.270156212 Simplifying r = 1.270156212Subproblem 2
r + -0.95 = -0.320156212 Simplifying r + -0.95 = -0.320156212 Reorder the terms: -0.95 + r = -0.320156212 Solving -0.95 + r = -0.320156212 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + r = -0.320156212 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + r = -0.320156212 + 0.95 r = -0.320156212 + 0.95 Combine like terms: -0.320156212 + 0.95 = 0.629843788 r = 0.629843788 Simplifying r = 0.629843788Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.270156212, 0.629843788}
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