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Simplifying 4r2 + 6r + -45 = 0 Reorder the terms: -45 + 6r + 4r2 = 0 Solving -45 + 6r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + 1.5r + r2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 1.5r + 11.25 + r2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 1.5r + r2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 1.5r + r2 = 0 + 11.25 1.5r + r2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 1.5r + r2 = 11.25 The r term is 1.5r. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5r + 0.5625 + r2 = 11.25 + 0.5625 Reorder the terms: 0.5625 + 1.5r + r2 = 11.25 + 0.5625 Combine like terms: 11.25 + 0.5625 = 11.8125 0.5625 + 1.5r + r2 = 11.8125 Factor a perfect square on the left side: (r + 0.75)(r + 0.75) = 11.8125 Calculate the square root of the right side: 3.436931771 Break this problem into two subproblems by setting (r + 0.75) equal to 3.436931771 and -3.436931771.Subproblem 1
r + 0.75 = 3.436931771 Simplifying r + 0.75 = 3.436931771 Reorder the terms: 0.75 + r = 3.436931771 Solving 0.75 + r = 3.436931771 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = 3.436931771 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = 3.436931771 + -0.75 r = 3.436931771 + -0.75 Combine like terms: 3.436931771 + -0.75 = 2.686931771 r = 2.686931771 Simplifying r = 2.686931771Subproblem 2
r + 0.75 = -3.436931771 Simplifying r + 0.75 = -3.436931771 Reorder the terms: 0.75 + r = -3.436931771 Solving 0.75 + r = -3.436931771 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = -3.436931771 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = -3.436931771 + -0.75 r = -3.436931771 + -0.75 Combine like terms: -3.436931771 + -0.75 = -4.186931771 r = -4.186931771 Simplifying r = -4.186931771Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.686931771, -4.186931771}
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