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Simplifying 4r2 + -36r + 49 = 0 Reorder the terms: 49 + -36r + 4r2 = 0 Solving 49 + -36r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.25 + -9r + r2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -9r + -12.25 + r2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -9r + r2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -9r + r2 = 0 + -12.25 -9r + r2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -9r + r2 = -12.25 The r term is -9r. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9r + 20.25 + r2 = -12.25 + 20.25 Reorder the terms: 20.25 + -9r + r2 = -12.25 + 20.25 Combine like terms: -12.25 + 20.25 = 8 20.25 + -9r + r2 = 8 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (r + -4.5) equal to 2.828427125 and -2.828427125.Subproblem 1
r + -4.5 = 2.828427125 Simplifying r + -4.5 = 2.828427125 Reorder the terms: -4.5 + r = 2.828427125 Solving -4.5 + r = 2.828427125 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 2.828427125 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 2.828427125 + 4.5 r = 2.828427125 + 4.5 Combine like terms: 2.828427125 + 4.5 = 7.328427125 r = 7.328427125 Simplifying r = 7.328427125Subproblem 2
r + -4.5 = -2.828427125 Simplifying r + -4.5 = -2.828427125 Reorder the terms: -4.5 + r = -2.828427125 Solving -4.5 + r = -2.828427125 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -2.828427125 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -2.828427125 + 4.5 r = -2.828427125 + 4.5 Combine like terms: -2.828427125 + 4.5 = 1.671572875 r = 1.671572875 Simplifying r = 1.671572875Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.328427125, 1.671572875}
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