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Simplifying 37r2 + 69r + -8 = 0 Reorder the terms: -8 + 69r + 37r2 = 0 Solving -8 + 69r + 37r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 37 the coefficient of the squared term: Divide each side by '37'. -0.2162162162 + 1.864864865r + r2 = 0 Move the constant term to the right: Add '0.2162162162' to each side of the equation. -0.2162162162 + 1.864864865r + 0.2162162162 + r2 = 0 + 0.2162162162 Reorder the terms: -0.2162162162 + 0.2162162162 + 1.864864865r + r2 = 0 + 0.2162162162 Combine like terms: -0.2162162162 + 0.2162162162 = 0.0000000000 0.0000000000 + 1.864864865r + r2 = 0 + 0.2162162162 1.864864865r + r2 = 0 + 0.2162162162 Combine like terms: 0 + 0.2162162162 = 0.2162162162 1.864864865r + r2 = 0.2162162162 The r term is 1.864864865r. Take half its coefficient (0.9324324325). Square it (0.8694302412) and add it to both sides. Add '0.8694302412' to each side of the equation. 1.864864865r + 0.8694302412 + r2 = 0.2162162162 + 0.8694302412 Reorder the terms: 0.8694302412 + 1.864864865r + r2 = 0.2162162162 + 0.8694302412 Combine like terms: 0.2162162162 + 0.8694302412 = 1.0856464574 0.8694302412 + 1.864864865r + r2 = 1.0856464574 Factor a perfect square on the left side: (r + 0.9324324325)(r + 0.9324324325) = 1.0856464574 Calculate the square root of the right side: 1.041943596 Break this problem into two subproblems by setting (r + 0.9324324325) equal to 1.041943596 and -1.041943596.Subproblem 1
r + 0.9324324325 = 1.041943596 Simplifying r + 0.9324324325 = 1.041943596 Reorder the terms: 0.9324324325 + r = 1.041943596 Solving 0.9324324325 + r = 1.041943596 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.9324324325' to each side of the equation. 0.9324324325 + -0.9324324325 + r = 1.041943596 + -0.9324324325 Combine like terms: 0.9324324325 + -0.9324324325 = 0.0000000000 0.0000000000 + r = 1.041943596 + -0.9324324325 r = 1.041943596 + -0.9324324325 Combine like terms: 1.041943596 + -0.9324324325 = 0.1095111635 r = 0.1095111635 Simplifying r = 0.1095111635Subproblem 2
r + 0.9324324325 = -1.041943596 Simplifying r + 0.9324324325 = -1.041943596 Reorder the terms: 0.9324324325 + r = -1.041943596 Solving 0.9324324325 + r = -1.041943596 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.9324324325' to each side of the equation. 0.9324324325 + -0.9324324325 + r = -1.041943596 + -0.9324324325 Combine like terms: 0.9324324325 + -0.9324324325 = 0.0000000000 0.0000000000 + r = -1.041943596 + -0.9324324325 r = -1.041943596 + -0.9324324325 Combine like terms: -1.041943596 + -0.9324324325 = -1.9743760285 r = -1.9743760285 Simplifying r = -1.9743760285Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.1095111635, -1.9743760285}
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