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Simplifying 8r2 = -4r + 16 Reorder the terms: 8r2 = 16 + -4r Solving 8r2 = 16 + -4r Solving for variable 'r'. Reorder the terms: -16 + 4r + 8r2 = 16 + -4r + -16 + 4r Reorder the terms: -16 + 4r + 8r2 = 16 + -16 + -4r + 4r Combine like terms: 16 + -16 = 0 -16 + 4r + 8r2 = 0 + -4r + 4r -16 + 4r + 8r2 = -4r + 4r Combine like terms: -4r + 4r = 0 -16 + 4r + 8r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + r + 2r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + r + 2r2)' equal to zero and attempt to solve: Simplifying -4 + r + 2r2 = 0 Solving -4 + r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 0.5r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5r + r2 = 0 + 2 0.5r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5r + r2 = 2 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5r + 0.25 + r2 = 2 + 0.25 Reorder the terms: 0.25 + 0.5r + r2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 0.25 + 0.5r + r2 = 2.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (r + 0.5) equal to 1.5 and -1.5.Subproblem 1
r + 0.5 = 1.5 Simplifying r + 0.5 = 1.5 Reorder the terms: 0.5 + r = 1.5 Solving 0.5 + r = 1.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 1.5 + -0.5 r = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 r = 1 Simplifying r = 1Subproblem 2
r + 0.5 = -1.5 Simplifying r + 0.5 = -1.5 Reorder the terms: 0.5 + r = -1.5 Solving 0.5 + r = -1.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -1.5 + -0.5 r = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 r = -2 Simplifying r = -2Solution
The solution to the problem is based on the solutions from the subproblems. r = {1, -2}Solution
r = {1, -2}
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