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Simplifying r2 + 40r + -180000 = 0 Reorder the terms: -180000 + 40r + r2 = 0 Solving -180000 + 40r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '180000' to each side of the equation. -180000 + 40r + 180000 + r2 = 0 + 180000 Reorder the terms: -180000 + 180000 + 40r + r2 = 0 + 180000 Combine like terms: -180000 + 180000 = 0 0 + 40r + r2 = 0 + 180000 40r + r2 = 0 + 180000 Combine like terms: 0 + 180000 = 180000 40r + r2 = 180000 The r term is 40r. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40r + 400 + r2 = 180000 + 400 Reorder the terms: 400 + 40r + r2 = 180000 + 400 Combine like terms: 180000 + 400 = 180400 400 + 40r + r2 = 180400 Factor a perfect square on the left side: (r + 20)(r + 20) = 180400 Calculate the square root of the right side: 424.735211632 Break this problem into two subproblems by setting (r + 20) equal to 424.735211632 and -424.735211632.Subproblem 1
r + 20 = 424.735211632 Simplifying r + 20 = 424.735211632 Reorder the terms: 20 + r = 424.735211632 Solving 20 + r = 424.735211632 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = 424.735211632 + -20 Combine like terms: 20 + -20 = 0 0 + r = 424.735211632 + -20 r = 424.735211632 + -20 Combine like terms: 424.735211632 + -20 = 404.735211632 r = 404.735211632 Simplifying r = 404.735211632Subproblem 2
r + 20 = -424.735211632 Simplifying r + 20 = -424.735211632 Reorder the terms: 20 + r = -424.735211632 Solving 20 + r = -424.735211632 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = -424.735211632 + -20 Combine like terms: 20 + -20 = 0 0 + r = -424.735211632 + -20 r = -424.735211632 + -20 Combine like terms: -424.735211632 + -20 = -444.735211632 r = -444.735211632 Simplifying r = -444.735211632Solution
The solution to the problem is based on the solutions from the subproblems. r = {404.735211632, -444.735211632}
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