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Simplifying 4r2 + -16r + -20 = -5 Reorder the terms: -20 + -16r + 4r2 = -5 Solving -20 + -16r + 4r2 = -5 Solving for variable 'r'. Reorder the terms: -20 + 5 + -16r + 4r2 = -5 + 5 Combine like terms: -20 + 5 = -15 -15 + -16r + 4r2 = -5 + 5 Combine like terms: -5 + 5 = 0 -15 + -16r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -4r + r2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -4r + 3.75 + r2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -4r + r2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -4r + r2 = 0 + 3.75 -4r + r2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -4r + r2 = 3.75 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 = 3.75 + 4 Reorder the terms: 4 + -4r + r2 = 3.75 + 4 Combine like terms: 3.75 + 4 = 7.75 4 + -4r + r2 = 7.75 Factor a perfect square on the left side: (r + -2)(r + -2) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (r + -2) equal to 2.783882181 and -2.783882181.Subproblem 1
r + -2 = 2.783882181 Simplifying r + -2 = 2.783882181 Reorder the terms: -2 + r = 2.783882181 Solving -2 + r = 2.783882181 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 = 2.783882181 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.783882181 + 2 r = 2.783882181 + 2 Combine like terms: 2.783882181 + 2 = 4.783882181 r = 4.783882181 Simplifying r = 4.783882181Subproblem 2
r + -2 = -2.783882181 Simplifying r + -2 = -2.783882181 Reorder the terms: -2 + r = -2.783882181 Solving -2 + r = -2.783882181 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 = -2.783882181 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.783882181 + 2 r = -2.783882181 + 2 Combine like terms: -2.783882181 + 2 = -0.783882181 r = -0.783882181 Simplifying r = -0.783882181Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.783882181, -0.783882181}
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