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Simplifying 2r(r + 4) = (r + -3)(r + -3) Reorder the terms: 2r(4 + r) = (r + -3)(r + -3) (4 * 2r + r * 2r) = (r + -3)(r + -3) (8r + 2r2) = (r + -3)(r + -3) Reorder the terms: 8r + 2r2 = (-3 + r)(r + -3) Reorder the terms: 8r + 2r2 = (-3 + r)(-3 + r) Multiply (-3 + r) * (-3 + r) 8r + 2r2 = (-3(-3 + r) + r(-3 + r)) 8r + 2r2 = ((-3 * -3 + r * -3) + r(-3 + r)) 8r + 2r2 = ((9 + -3r) + r(-3 + r)) 8r + 2r2 = (9 + -3r + (-3 * r + r * r)) 8r + 2r2 = (9 + -3r + (-3r + r2)) Combine like terms: -3r + -3r = -6r 8r + 2r2 = (9 + -6r + r2) Solving 8r + 2r2 = 9 + -6r + r2 Solving for variable 'r'. Reorder the terms: -9 + 8r + 6r + 2r2 + -1r2 = 9 + -6r + r2 + -9 + 6r + -1r2 Combine like terms: 8r + 6r = 14r -9 + 14r + 2r2 + -1r2 = 9 + -6r + r2 + -9 + 6r + -1r2 Combine like terms: 2r2 + -1r2 = 1r2 -9 + 14r + 1r2 = 9 + -6r + r2 + -9 + 6r + -1r2 Reorder the terms: -9 + 14r + 1r2 = 9 + -9 + -6r + 6r + r2 + -1r2 Combine like terms: 9 + -9 = 0 -9 + 14r + 1r2 = 0 + -6r + 6r + r2 + -1r2 -9 + 14r + 1r2 = -6r + 6r + r2 + -1r2 Combine like terms: -6r + 6r = 0 -9 + 14r + 1r2 = 0 + r2 + -1r2 -9 + 14r + 1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -9 + 14r + 1r2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 14r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + 14r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 14r + r2 = 0 + 9 14r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 14r + r2 = 9 The r term is 14r. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14r + 49 + r2 = 9 + 49 Reorder the terms: 49 + 14r + r2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + 14r + r2 = 58 Factor a perfect square on the left side: (r + 7)(r + 7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (r + 7) equal to 7.615773106 and -7.615773106.Subproblem 1
r + 7 = 7.615773106 Simplifying r + 7 = 7.615773106 Reorder the terms: 7 + r = 7.615773106 Solving 7 + r = 7.615773106 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + r = 7.615773106 + -7 r = 7.615773106 + -7 Combine like terms: 7.615773106 + -7 = 0.615773106 r = 0.615773106 Simplifying r = 0.615773106Subproblem 2
r + 7 = -7.615773106 Simplifying r + 7 = -7.615773106 Reorder the terms: 7 + r = -7.615773106 Solving 7 + r = -7.615773106 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + r = -7.615773106 + -7 r = -7.615773106 + -7 Combine like terms: -7.615773106 + -7 = -14.615773106 r = -14.615773106 Simplifying r = -14.615773106Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.615773106, -14.615773106}
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