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Simplifying 2r2 + -1r + -5.25 = 0 Reorder the terms: -5.25 + -1r + 2r2 = 0 Solving -5.25 + -1r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.625 + -0.5r + r2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -0.5r + 2.625 + r2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -0.5r + r2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -0.5r + r2 = 0 + 2.625 -0.5r + r2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -0.5r + r2 = 2.625 The r term is -0.5r. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5r + 0.0625 + r2 = 2.625 + 0.0625 Reorder the terms: 0.0625 + -0.5r + r2 = 2.625 + 0.0625 Combine like terms: 2.625 + 0.0625 = 2.6875 0.0625 + -0.5r + r2 = 2.6875 Factor a perfect square on the left side: (r + -0.25)(r + -0.25) = 2.6875 Calculate the square root of the right side: 1.639359631 Break this problem into two subproblems by setting (r + -0.25) equal to 1.639359631 and -1.639359631.Subproblem 1
r + -0.25 = 1.639359631 Simplifying r + -0.25 = 1.639359631 Reorder the terms: -0.25 + r = 1.639359631 Solving -0.25 + r = 1.639359631 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + r = 1.639359631 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + r = 1.639359631 + 0.25 r = 1.639359631 + 0.25 Combine like terms: 1.639359631 + 0.25 = 1.889359631 r = 1.889359631 Simplifying r = 1.889359631Subproblem 2
r + -0.25 = -1.639359631 Simplifying r + -0.25 = -1.639359631 Reorder the terms: -0.25 + r = -1.639359631 Solving -0.25 + r = -1.639359631 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + r = -1.639359631 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + r = -1.639359631 + 0.25 r = -1.639359631 + 0.25 Combine like terms: -1.639359631 + 0.25 = -1.389359631 r = -1.389359631 Simplifying r = -1.389359631Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.889359631, -1.389359631}
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