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Simplifying 7r2 + 48r + 7 = 0 Reorder the terms: 7 + 48r + 7r2 = 0 Solving 7 + 48r + 7r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + 6.857142857r + r2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 6.857142857r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + 6.857142857r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6.857142857r + r2 = 0 + -1 6.857142857r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 6.857142857r + r2 = -1 The r term is 6.857142857r. Take half its coefficient (3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. 6.857142857r + 11.75510204 + r2 = -1 + 11.75510204 Reorder the terms: 11.75510204 + 6.857142857r + r2 = -1 + 11.75510204 Combine like terms: -1 + 11.75510204 = 10.75510204 11.75510204 + 6.857142857r + r2 = 10.75510204 Factor a perfect square on the left side: (r + 3.428571429)(r + 3.428571429) = 10.75510204 Calculate the square root of the right side: 3.279497224 Break this problem into two subproblems by setting (r + 3.428571429) equal to 3.279497224 and -3.279497224.Subproblem 1
r + 3.428571429 = 3.279497224 Simplifying r + 3.428571429 = 3.279497224 Reorder the terms: 3.428571429 + r = 3.279497224 Solving 3.428571429 + r = 3.279497224 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + r = 3.279497224 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + r = 3.279497224 + -3.428571429 r = 3.279497224 + -3.428571429 Combine like terms: 3.279497224 + -3.428571429 = -0.149074205 r = -0.149074205 Simplifying r = -0.149074205Subproblem 2
r + 3.428571429 = -3.279497224 Simplifying r + 3.428571429 = -3.279497224 Reorder the terms: 3.428571429 + r = -3.279497224 Solving 3.428571429 + r = -3.279497224 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + r = -3.279497224 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + r = -3.279497224 + -3.428571429 r = -3.279497224 + -3.428571429 Combine like terms: -3.279497224 + -3.428571429 = -6.708068653 r = -6.708068653 Simplifying r = -6.708068653Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.149074205, -6.708068653}
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