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Simplifying -6r + 2r(r + 2) + -5 = 20 Reorder the terms: -6r + 2r(2 + r) + -5 = 20 -6r + (2 * 2r + r * 2r) + -5 = 20 -6r + (4r + 2r2) + -5 = 20 Reorder the terms: -5 + -6r + 4r + 2r2 = 20 Combine like terms: -6r + 4r = -2r -5 + -2r + 2r2 = 20 Solving -5 + -2r + 2r2 = 20 Solving for variable 'r'. Reorder the terms: -5 + -20 + -2r + 2r2 = 20 + -20 Combine like terms: -5 + -20 = -25 -25 + -2r + 2r2 = 20 + -20 Combine like terms: 20 + -20 = 0 -25 + -2r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -1r + r2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1r + 12.5 + r2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1r + r2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1r + r2 = 0 + 12.5 -1r + r2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1r + r2 = 12.5 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 12.5 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 0.25 + -1r + r2 = 12.75 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (r + -0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
r + -0.5 = 3.570714214 Simplifying r + -0.5 = 3.570714214 Reorder the terms: -0.5 + r = 3.570714214 Solving -0.5 + r = 3.570714214 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 3.570714214 + 0.5 r = 3.570714214 + 0.5 Combine like terms: 3.570714214 + 0.5 = 4.070714214 r = 4.070714214 Simplifying r = 4.070714214Subproblem 2
r + -0.5 = -3.570714214 Simplifying r + -0.5 = -3.570714214 Reorder the terms: -0.5 + r = -3.570714214 Solving -0.5 + r = -3.570714214 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -3.570714214 + 0.5 r = -3.570714214 + 0.5 Combine like terms: -3.570714214 + 0.5 = -3.070714214 r = -3.070714214 Simplifying r = -3.070714214Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.070714214, -3.070714214}
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