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Simplifying 7r2 + -28r + -21 = 3 Reorder the terms: -21 + -28r + 7r2 = 3 Solving -21 + -28r + 7r2 = 3 Solving for variable 'r'. Reorder the terms: -21 + -3 + -28r + 7r2 = 3 + -3 Combine like terms: -21 + -3 = -24 -24 + -28r + 7r2 = 3 + -3 Combine like terms: 3 + -3 = 0 -24 + -28r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -4r + r2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -4r + 3.428571429 + r2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -4r + r2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -4r + r2 = 0 + 3.428571429 -4r + r2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -4r + r2 = 3.428571429 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 3.428571429 + 4 Reorder the terms: 4 + -4r + r2 = 3.428571429 + 4 Combine like terms: 3.428571429 + 4 = 7.428571429 4 + -4r + r2 = 7.428571429 Factor a perfect square on the left side: (r + -2)(r + -2) = 7.428571429 Calculate the square root of the right side: 2.725540576 Break this problem into two subproblems by setting (r + -2) equal to 2.725540576 and -2.725540576.Subproblem 1
r + -2 = 2.725540576 Simplifying r + -2 = 2.725540576 Reorder the terms: -2 + r = 2.725540576 Solving -2 + r = 2.725540576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 2.725540576 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.725540576 + 2 r = 2.725540576 + 2 Combine like terms: 2.725540576 + 2 = 4.725540576 r = 4.725540576 Simplifying r = 4.725540576Subproblem 2
r + -2 = -2.725540576 Simplifying r + -2 = -2.725540576 Reorder the terms: -2 + r = -2.725540576 Solving -2 + r = -2.725540576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -2.725540576 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.725540576 + 2 r = -2.725540576 + 2 Combine like terms: -2.725540576 + 2 = -0.725540576 r = -0.725540576 Simplifying r = -0.725540576Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.725540576, -0.725540576}
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