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Simplifying -7r2 + -20r + 100 = 0 Reorder the terms: 100 + -20r + -7r2 = 0 Solving 100 + -20r + -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'. -14.28571429 + 2.857142857r + r2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + 2.857142857r + 14.28571429 + r2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + 2.857142857r + r2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + 2.857142857r + r2 = 0 + 14.28571429 2.857142857r + r2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 2.857142857r + r2 = 14.28571429 The r term is 2.857142857r. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857r + 2.040816328 + r2 = 14.28571429 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857r + r2 = 14.28571429 + 2.040816328 Combine like terms: 14.28571429 + 2.040816328 = 16.326530618 2.040816328 + 2.857142857r + r2 = 16.326530618 Factor a perfect square on the left side: (r + 1.428571429)(r + 1.428571429) = 16.326530618 Calculate the square root of the right side: 4.040610179 Break this problem into two subproblems by setting (r + 1.428571429) equal to 4.040610179 and -4.040610179.Subproblem 1
r + 1.428571429 = 4.040610179 Simplifying r + 1.428571429 = 4.040610179 Reorder the terms: 1.428571429 + r = 4.040610179 Solving 1.428571429 + r = 4.040610179 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + r = 4.040610179 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + r = 4.040610179 + -1.428571429 r = 4.040610179 + -1.428571429 Combine like terms: 4.040610179 + -1.428571429 = 2.61203875 r = 2.61203875 Simplifying r = 2.61203875Subproblem 2
r + 1.428571429 = -4.040610179 Simplifying r + 1.428571429 = -4.040610179 Reorder the terms: 1.428571429 + r = -4.040610179 Solving 1.428571429 + r = -4.040610179 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + r = -4.040610179 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + r = -4.040610179 + -1.428571429 r = -4.040610179 + -1.428571429 Combine like terms: -4.040610179 + -1.428571429 = -5.469181608 r = -5.469181608 Simplifying r = -5.469181608Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.61203875, -5.469181608}
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