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Simplifying r2 + 4r + 7 = 14 Reorder the terms: 7 + 4r + r2 = 14 Solving 7 + 4r + r2 = 14 Solving for variable 'r'. Reorder the terms: 7 + -14 + 4r + r2 = 14 + -14 Combine like terms: 7 + -14 = -7 -7 + 4r + r2 = 14 + -14 Combine like terms: 14 + -14 = 0 -7 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 4r + 7 + r2 = 0 + 7 Reorder the terms: -7 + 7 + 4r + r2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4r + r2 = 0 + 7 4r + r2 = 0 + 7 Combine like terms: 0 + 7 = 7 4r + r2 = 7 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 = 7 + 4 Reorder the terms: 4 + 4r + r2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + 4r + r2 = 11 Factor a perfect square on the left side: (r + 2)(r + 2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (r + 2) equal to 3.31662479 and -3.31662479.Subproblem 1
r + 2 = 3.31662479 Simplifying r + 2 = 3.31662479 Reorder the terms: 2 + r = 3.31662479 Solving 2 + r = 3.31662479 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 = 3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + r = 3.31662479 + -2 r = 3.31662479 + -2 Combine like terms: 3.31662479 + -2 = 1.31662479 r = 1.31662479 Simplifying r = 1.31662479Subproblem 2
r + 2 = -3.31662479 Simplifying r + 2 = -3.31662479 Reorder the terms: 2 + r = -3.31662479 Solving 2 + r = -3.31662479 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 = -3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + r = -3.31662479 + -2 r = -3.31662479 + -2 Combine like terms: -3.31662479 + -2 = -5.31662479 r = -5.31662479 Simplifying r = -5.31662479Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.31662479, -5.31662479}
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