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Simplifying r2 + 15r + 10 = 0 Reorder the terms: 10 + 15r + r2 = 0 Solving 10 + 15r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 15r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + 15r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 15r + r2 = 0 + -10 15r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 15r + r2 = -10 The r term is 15r. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15r + 56.25 + r2 = -10 + 56.25 Reorder the terms: 56.25 + 15r + r2 = -10 + 56.25 Combine like terms: -10 + 56.25 = 46.25 56.25 + 15r + r2 = 46.25 Factor a perfect square on the left side: (r + 7.5)(r + 7.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (r + 7.5) equal to 6.800735254 and -6.800735254.Subproblem 1
r + 7.5 = 6.800735254 Simplifying r + 7.5 = 6.800735254 Reorder the terms: 7.5 + r = 6.800735254 Solving 7.5 + r = 6.800735254 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = 6.800735254 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 6.800735254 + -7.5 r = 6.800735254 + -7.5 Combine like terms: 6.800735254 + -7.5 = -0.699264746 r = -0.699264746 Simplifying r = -0.699264746Subproblem 2
r + 7.5 = -6.800735254 Simplifying r + 7.5 = -6.800735254 Reorder the terms: 7.5 + r = -6.800735254 Solving 7.5 + r = -6.800735254 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = -6.800735254 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -6.800735254 + -7.5 r = -6.800735254 + -7.5 Combine like terms: -6.800735254 + -7.5 = -14.300735254 r = -14.300735254 Simplifying r = -14.300735254Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.699264746, -14.300735254}
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