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Simplifying 8r + 3r + 2 = 7r2 Reorder the terms: 2 + 8r + 3r = 7r2 Combine like terms: 8r + 3r = 11r 2 + 11r = 7r2 Solving 2 + 11r = 7r2 Solving for variable 'r'. Combine like terms: 7r2 + -7r2 = 0 2 + 11r + -7r2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.2857142857 + -1.571428571r + r2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1.571428571r + 0.2857142857 + r2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1.571428571r + r2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1.571428571r + r2 = 0 + 0.2857142857 -1.571428571r + r2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1.571428571r + r2 = 0.2857142857 The r term is -1.571428571r. Take half its coefficient (-0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. -1.571428571r + 0.6173469384 + r2 = 0.2857142857 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571r + r2 = 0.2857142857 + 0.6173469384 Combine like terms: 0.2857142857 + 0.6173469384 = 0.9030612241 0.6173469384 + -1.571428571r + r2 = 0.9030612241 Factor a perfect square on the left side: (r + -0.7857142855)(r + -0.7857142855) = 0.9030612241 Calculate the square root of the right side: 0.950295335 Break this problem into two subproblems by setting (r + -0.7857142855) equal to 0.950295335 and -0.950295335.Subproblem 1
r + -0.7857142855 = 0.950295335 Simplifying r + -0.7857142855 = 0.950295335 Reorder the terms: -0.7857142855 + r = 0.950295335 Solving -0.7857142855 + r = 0.950295335 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + r = 0.950295335 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + r = 0.950295335 + 0.7857142855 r = 0.950295335 + 0.7857142855 Combine like terms: 0.950295335 + 0.7857142855 = 1.7360096205 r = 1.7360096205 Simplifying r = 1.7360096205Subproblem 2
r + -0.7857142855 = -0.950295335 Simplifying r + -0.7857142855 = -0.950295335 Reorder the terms: -0.7857142855 + r = -0.950295335 Solving -0.7857142855 + r = -0.950295335 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + r = -0.950295335 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + r = -0.950295335 + 0.7857142855 r = -0.950295335 + 0.7857142855 Combine like terms: -0.950295335 + 0.7857142855 = -0.1645810495 r = -0.1645810495 Simplifying r = -0.1645810495Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.7360096205, -0.1645810495}
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