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Simplifying -2r2 + 11r + 15 = 0 Reorder the terms: 15 + 11r + -2r2 = 0 Solving 15 + 11r + -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'. -7.5 + -5.5r + r2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5.5r + 7.5 + r2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5.5r + r2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5.5r + r2 = 0 + 7.5 -5.5r + r2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5.5r + r2 = 7.5 The r term is -5.5r. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5r + 7.5625 + r2 = 7.5 + 7.5625 Reorder the terms: 7.5625 + -5.5r + r2 = 7.5 + 7.5625 Combine like terms: 7.5 + 7.5625 = 15.0625 7.5625 + -5.5r + r2 = 15.0625 Factor a perfect square on the left side: (r + -2.75)(r + -2.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (r + -2.75) equal to 3.881043674 and -3.881043674.Subproblem 1
r + -2.75 = 3.881043674 Simplifying r + -2.75 = 3.881043674 Reorder the terms: -2.75 + r = 3.881043674 Solving -2.75 + r = 3.881043674 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = 3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = 3.881043674 + 2.75 r = 3.881043674 + 2.75 Combine like terms: 3.881043674 + 2.75 = 6.631043674 r = 6.631043674 Simplifying r = 6.631043674Subproblem 2
r + -2.75 = -3.881043674 Simplifying r + -2.75 = -3.881043674 Reorder the terms: -2.75 + r = -3.881043674 Solving -2.75 + r = -3.881043674 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = -3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = -3.881043674 + 2.75 r = -3.881043674 + 2.75 Combine like terms: -3.881043674 + 2.75 = -1.131043674 r = -1.131043674 Simplifying r = -1.131043674Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.631043674, -1.131043674}
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