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Simplifying 2r2 = -8r + 3 Reorder the terms: 2r2 = 3 + -8r Solving 2r2 = 3 + -8r Solving for variable 'r'. Reorder the terms: -3 + 8r + 2r2 = 3 + -8r + -3 + 8r Reorder the terms: -3 + 8r + 2r2 = 3 + -3 + -8r + 8r Combine like terms: 3 + -3 = 0 -3 + 8r + 2r2 = 0 + -8r + 8r -3 + 8r + 2r2 = -8r + 8r Combine like terms: -8r + 8r = 0 -3 + 8r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 4r + r2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4r + 1.5 + r2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4r + r2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4r + r2 = 0 + 1.5 4r + r2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4r + r2 = 1.5 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 1.5 + 4 Reorder the terms: 4 + 4r + r2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + 4r + r2 = 5.5 Factor a perfect square on the left side: (r + 2)(r + 2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (r + 2) equal to 2.34520788 and -2.34520788.Subproblem 1
r + 2 = 2.34520788 Simplifying r + 2 = 2.34520788 Reorder the terms: 2 + r = 2.34520788 Solving 2 + r = 2.34520788 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + r = 2.34520788 + -2 r = 2.34520788 + -2 Combine like terms: 2.34520788 + -2 = 0.34520788 r = 0.34520788 Simplifying r = 0.34520788Subproblem 2
r + 2 = -2.34520788 Simplifying r + 2 = -2.34520788 Reorder the terms: 2 + r = -2.34520788 Solving 2 + r = -2.34520788 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + r = -2.34520788 + -2 r = -2.34520788 + -2 Combine like terms: -2.34520788 + -2 = -4.34520788 r = -4.34520788 Simplifying r = -4.34520788Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.34520788, -4.34520788}
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