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Simplifying 4r2 = 12r + 5 Reorder the terms: 4r2 = 5 + 12r Solving 4r2 = 5 + 12r Solving for variable 'r'. Reorder the terms: -5 + -12r + 4r2 = 5 + 12r + -5 + -12r Reorder the terms: -5 + -12r + 4r2 = 5 + -5 + 12r + -12r Combine like terms: 5 + -5 = 0 -5 + -12r + 4r2 = 0 + 12r + -12r -5 + -12r + 4r2 = 12r + -12r Combine like terms: 12r + -12r = 0 -5 + -12r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -3r + r2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3r + 1.25 + r2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3r + r2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3r + r2 = 0 + 1.25 -3r + r2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3r + r2 = 1.25 The r term is -3r. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3r + 2.25 + r2 = 1.25 + 2.25 Reorder the terms: 2.25 + -3r + r2 = 1.25 + 2.25 Combine like terms: 1.25 + 2.25 = 3.5 2.25 + -3r + r2 = 3.5 Factor a perfect square on the left side: (r + -1.5)(r + -1.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (r + -1.5) equal to 1.870828693 and -1.870828693.Subproblem 1
r + -1.5 = 1.870828693 Simplifying r + -1.5 = 1.870828693 Reorder the terms: -1.5 + r = 1.870828693 Solving -1.5 + r = 1.870828693 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = 1.870828693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = 1.870828693 + 1.5 r = 1.870828693 + 1.5 Combine like terms: 1.870828693 + 1.5 = 3.370828693 r = 3.370828693 Simplifying r = 3.370828693Subproblem 2
r + -1.5 = -1.870828693 Simplifying r + -1.5 = -1.870828693 Reorder the terms: -1.5 + r = -1.870828693 Solving -1.5 + r = -1.870828693 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = -1.870828693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = -1.870828693 + 1.5 r = -1.870828693 + 1.5 Combine like terms: -1.870828693 + 1.5 = -0.370828693 r = -0.370828693 Simplifying r = -0.370828693Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.370828693, -0.370828693}
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