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Simplifying 7r2 = 70r + -145 Reorder the terms: 7r2 = -145 + 70r Solving 7r2 = -145 + 70r Solving for variable 'r'. Reorder the terms: 145 + -70r + 7r2 = -145 + 70r + 145 + -70r Reorder the terms: 145 + -70r + 7r2 = -145 + 145 + 70r + -70r Combine like terms: -145 + 145 = 0 145 + -70r + 7r2 = 0 + 70r + -70r 145 + -70r + 7r2 = 70r + -70r Combine like terms: 70r + -70r = 0 145 + -70r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 20.71428571 + -10r + r2 = 0 Move the constant term to the right: Add '-20.71428571' to each side of the equation. 20.71428571 + -10r + -20.71428571 + r2 = 0 + -20.71428571 Reorder the terms: 20.71428571 + -20.71428571 + -10r + r2 = 0 + -20.71428571 Combine like terms: 20.71428571 + -20.71428571 = 0.00000000 0.00000000 + -10r + r2 = 0 + -20.71428571 -10r + r2 = 0 + -20.71428571 Combine like terms: 0 + -20.71428571 = -20.71428571 -10r + r2 = -20.71428571 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = -20.71428571 + 25 Reorder the terms: 25 + -10r + r2 = -20.71428571 + 25 Combine like terms: -20.71428571 + 25 = 4.28571429 25 + -10r + r2 = 4.28571429 Factor a perfect square on the left side: (r + -5)(r + -5) = 4.28571429 Calculate the square root of the right side: 2.070196679 Break this problem into two subproblems by setting (r + -5) equal to 2.070196679 and -2.070196679.Subproblem 1
r + -5 = 2.070196679 Simplifying r + -5 = 2.070196679 Reorder the terms: -5 + r = 2.070196679 Solving -5 + r = 2.070196679 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 2.070196679 + 5 Combine like terms: -5 + 5 = 0 0 + r = 2.070196679 + 5 r = 2.070196679 + 5 Combine like terms: 2.070196679 + 5 = 7.070196679 r = 7.070196679 Simplifying r = 7.070196679Subproblem 2
r + -5 = -2.070196679 Simplifying r + -5 = -2.070196679 Reorder the terms: -5 + r = -2.070196679 Solving -5 + r = -2.070196679 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -2.070196679 + 5 Combine like terms: -5 + 5 = 0 0 + r = -2.070196679 + 5 r = -2.070196679 + 5 Combine like terms: -2.070196679 + 5 = 2.929803321 r = 2.929803321 Simplifying r = 2.929803321Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.070196679, 2.929803321}
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