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Simplifying r2 + 4r + -84 = 0 Reorder the terms: -84 + 4r + r2 = 0 Solving -84 + 4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 4r + 84 + r2 = 0 + 84 Reorder the terms: -84 + 84 + 4r + r2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 4r + r2 = 0 + 84 4r + r2 = 0 + 84 Combine like terms: 0 + 84 = 84 4r + r2 = 84 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 84 + 4 Reorder the terms: 4 + 4r + r2 = 84 + 4 Combine like terms: 84 + 4 = 88 4 + 4r + r2 = 88 Factor a perfect square on the left side: (r + 2)(r + 2) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (r + 2) equal to 9.38083152 and -9.38083152.Subproblem 1
r + 2 = 9.38083152 Simplifying r + 2 = 9.38083152 Reorder the terms: 2 + r = 9.38083152 Solving 2 + r = 9.38083152 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 9.38083152 + -2 Combine like terms: 2 + -2 = 0 0 + r = 9.38083152 + -2 r = 9.38083152 + -2 Combine like terms: 9.38083152 + -2 = 7.38083152 r = 7.38083152 Simplifying r = 7.38083152Subproblem 2
r + 2 = -9.38083152 Simplifying r + 2 = -9.38083152 Reorder the terms: 2 + r = -9.38083152 Solving 2 + r = -9.38083152 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -9.38083152 + -2 Combine like terms: 2 + -2 = 0 0 + r = -9.38083152 + -2 r = -9.38083152 + -2 Combine like terms: -9.38083152 + -2 = -11.38083152 r = -11.38083152 Simplifying r = -11.38083152Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.38083152, -11.38083152}
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