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Simplifying 4r2 + 28r + 16 = 0 Reorder the terms: 16 + 28r + 4r2 = 0 Solving 16 + 28r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 7r + r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + 7r + r2)' equal to zero and attempt to solve: Simplifying 4 + 7r + r2 = 0 Solving 4 + 7r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7r + -4 + r2 = 0 + -4 Reorder the terms: 4 + -4 + 7r + r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7r + r2 = 0 + -4 7r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 7r + r2 = -4 The r term is 7r. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7r + 12.25 + r2 = -4 + 12.25 Reorder the terms: 12.25 + 7r + r2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + 7r + r2 = 8.25 Factor a perfect square on the left side: (r + 3.5)(r + 3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (r + 3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
r + 3.5 = 2.872281323 Simplifying r + 3.5 = 2.872281323 Reorder the terms: 3.5 + r = 2.872281323 Solving 3.5 + r = 2.872281323 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + r = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = 2.872281323 + -3.5 r = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 r = -0.627718677 Simplifying r = -0.627718677Subproblem 2
r + 3.5 = -2.872281323 Simplifying r + 3.5 = -2.872281323 Reorder the terms: 3.5 + r = -2.872281323 Solving 3.5 + r = -2.872281323 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + r = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = -2.872281323 + -3.5 r = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 r = -6.372281323 Simplifying r = -6.372281323Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.627718677, -6.372281323}Solution
r = {-0.627718677, -6.372281323}
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