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Simplifying r2 + 15r + -4752 = 0 Reorder the terms: -4752 + 15r + r2 = 0 Solving -4752 + 15r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '4752' to each side of the equation. -4752 + 15r + 4752 + r2 = 0 + 4752 Reorder the terms: -4752 + 4752 + 15r + r2 = 0 + 4752 Combine like terms: -4752 + 4752 = 0 0 + 15r + r2 = 0 + 4752 15r + r2 = 0 + 4752 Combine like terms: 0 + 4752 = 4752 15r + r2 = 4752 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 = 4752 + 56.25 Reorder the terms: 56.25 + 15r + r2 = 4752 + 56.25 Combine like terms: 4752 + 56.25 = 4808.25 56.25 + 15r + r2 = 4808.25 Factor a perfect square on the left side: (r + 7.5)(r + 7.5) = 4808.25 Calculate the square root of the right side: 69.341545988 Break this problem into two subproblems by setting (r + 7.5) equal to 69.341545988 and -69.341545988.Subproblem 1
r + 7.5 = 69.341545988 Simplifying r + 7.5 = 69.341545988 Reorder the terms: 7.5 + r = 69.341545988 Solving 7.5 + r = 69.341545988 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 = 69.341545988 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 69.341545988 + -7.5 r = 69.341545988 + -7.5 Combine like terms: 69.341545988 + -7.5 = 61.841545988 r = 61.841545988 Simplifying r = 61.841545988Subproblem 2
r + 7.5 = -69.341545988 Simplifying r + 7.5 = -69.341545988 Reorder the terms: 7.5 + r = -69.341545988 Solving 7.5 + r = -69.341545988 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 = -69.341545988 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -69.341545988 + -7.5 r = -69.341545988 + -7.5 Combine like terms: -69.341545988 + -7.5 = -76.841545988 r = -76.841545988 Simplifying r = -76.841545988Solution
The solution to the problem is based on the solutions from the subproblems. r = {61.841545988, -76.841545988}
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