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Simplifying -14r2 + 90r = -686 Reorder the terms: 90r + -14r2 = -686 Solving 90r + -14r2 = -686 Solving for variable 'r'. Reorder the terms: 686 + 90r + -14r2 = -686 + 686 Combine like terms: -686 + 686 = 0 686 + 90r + -14r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(343 + 45r + -7r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(343 + 45r + -7r2)' equal to zero and attempt to solve: Simplifying 343 + 45r + -7r2 = 0 Solving 343 + 45r + -7r2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -49 + -6.428571429r + r2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -6.428571429r + 49 + r2 = 0 + 49 Reorder the terms: -49 + 49 + -6.428571429r + r2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -6.428571429r + r2 = 0 + 49 -6.428571429r + r2 = 0 + 49 Combine like terms: 0 + 49 = 49 -6.428571429r + r2 = 49 The r term is -6.428571429r. Take half its coefficient (-3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. -6.428571429r + 10.33163266 + r2 = 49 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429r + r2 = 49 + 10.33163266 Combine like terms: 49 + 10.33163266 = 59.33163266 10.33163266 + -6.428571429r + r2 = 59.33163266 Factor a perfect square on the left side: (r + -3.214285715)(r + -3.214285715) = 59.33163266 Calculate the square root of the right side: 7.702702945 Break this problem into two subproblems by setting (r + -3.214285715) equal to 7.702702945 and -7.702702945.Subproblem 1
r + -3.214285715 = 7.702702945 Simplifying r + -3.214285715 = 7.702702945 Reorder the terms: -3.214285715 + r = 7.702702945 Solving -3.214285715 + r = 7.702702945 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + r = 7.702702945 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + r = 7.702702945 + 3.214285715 r = 7.702702945 + 3.214285715 Combine like terms: 7.702702945 + 3.214285715 = 10.91698866 r = 10.91698866 Simplifying r = 10.91698866Subproblem 2
r + -3.214285715 = -7.702702945 Simplifying r + -3.214285715 = -7.702702945 Reorder the terms: -3.214285715 + r = -7.702702945 Solving -3.214285715 + r = -7.702702945 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + r = -7.702702945 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + r = -7.702702945 + 3.214285715 r = -7.702702945 + 3.214285715 Combine like terms: -7.702702945 + 3.214285715 = -4.48841723 r = -4.48841723 Simplifying r = -4.48841723Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.91698866, -4.48841723}Solution
r = {10.91698866, -4.48841723}
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