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Simplifying 5r2 + -20r + -144 = 0 Reorder the terms: -144 + -20r + 5r2 = 0 Solving -144 + -20r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -28.8 + -4r + r2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + -4r + 28.8 + r2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + -4r + r2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + -4r + r2 = 0 + 28.8 -4r + r2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 -4r + r2 = 28.8 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 = 28.8 + 4 Reorder the terms: 4 + -4r + r2 = 28.8 + 4 Combine like terms: 28.8 + 4 = 32.8 4 + -4r + r2 = 32.8 Factor a perfect square on the left side: (r + -2)(r + -2) = 32.8 Calculate the square root of the right side: 5.727128425 Break this problem into two subproblems by setting (r + -2) equal to 5.727128425 and -5.727128425.Subproblem 1
r + -2 = 5.727128425 Simplifying r + -2 = 5.727128425 Reorder the terms: -2 + r = 5.727128425 Solving -2 + r = 5.727128425 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 = 5.727128425 + 2 Combine like terms: -2 + 2 = 0 0 + r = 5.727128425 + 2 r = 5.727128425 + 2 Combine like terms: 5.727128425 + 2 = 7.727128425 r = 7.727128425 Simplifying r = 7.727128425Subproblem 2
r + -2 = -5.727128425 Simplifying r + -2 = -5.727128425 Reorder the terms: -2 + r = -5.727128425 Solving -2 + r = -5.727128425 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 = -5.727128425 + 2 Combine like terms: -2 + 2 = 0 0 + r = -5.727128425 + 2 r = -5.727128425 + 2 Combine like terms: -5.727128425 + 2 = -3.727128425 r = -3.727128425 Simplifying r = -3.727128425Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.727128425, -3.727128425}
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