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Simplifying 2r + -3 = r * r + -2r + -0.25 Reorder the terms: -3 + 2r = r * r + -2r + -0.25 Multiply r * r -3 + 2r = r2 + -2r + -0.25 Reorder the terms: -3 + 2r = -0.25 + -2r + r2 Solving -3 + 2r = -0.25 + -2r + r2 Solving for variable 'r'. Reorder the terms: -3 + 0.25 + 2r + 2r + -1r2 = -0.25 + -2r + r2 + 0.25 + 2r + -1r2 Combine like terms: -3 + 0.25 = -2.75 -2.75 + 2r + 2r + -1r2 = -0.25 + -2r + r2 + 0.25 + 2r + -1r2 Combine like terms: 2r + 2r = 4r -2.75 + 4r + -1r2 = -0.25 + -2r + r2 + 0.25 + 2r + -1r2 Reorder the terms: -2.75 + 4r + -1r2 = -0.25 + 0.25 + -2r + 2r + r2 + -1r2 Combine like terms: -0.25 + 0.25 = 0.00 -2.75 + 4r + -1r2 = 0.00 + -2r + 2r + r2 + -1r2 -2.75 + 4r + -1r2 = -2r + 2r + r2 + -1r2 Combine like terms: -2r + 2r = 0 -2.75 + 4r + -1r2 = 0 + r2 + -1r2 -2.75 + 4r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -2.75 + 4r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.75 + -4r + r2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -4r + -2.75 + r2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -4r + r2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -4r + r2 = 0 + -2.75 -4r + r2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -4r + r2 = -2.75 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 = -2.75 + 4 Reorder the terms: 4 + -4r + r2 = -2.75 + 4 Combine like terms: -2.75 + 4 = 1.25 4 + -4r + r2 = 1.25 Factor a perfect square on the left side: (r + -2)(r + -2) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (r + -2) equal to 1.118033989 and -1.118033989.Subproblem 1
r + -2 = 1.118033989 Simplifying r + -2 = 1.118033989 Reorder the terms: -2 + r = 1.118033989 Solving -2 + r = 1.118033989 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 = 1.118033989 + 2 Combine like terms: -2 + 2 = 0 0 + r = 1.118033989 + 2 r = 1.118033989 + 2 Combine like terms: 1.118033989 + 2 = 3.118033989 r = 3.118033989 Simplifying r = 3.118033989Subproblem 2
r + -2 = -1.118033989 Simplifying r + -2 = -1.118033989 Reorder the terms: -2 + r = -1.118033989 Solving -2 + r = -1.118033989 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 = -1.118033989 + 2 Combine like terms: -2 + 2 = 0 0 + r = -1.118033989 + 2 r = -1.118033989 + 2 Combine like terms: -1.118033989 + 2 = 0.881966011 r = 0.881966011 Simplifying r = 0.881966011Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.118033989, 0.881966011}
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