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Simplifying (-1r2) + 4(-1r) + -4 = -8 Remove parenthesis around (-1r) (-1r2) + 4 * -1r + -4 = -8 Multiply 4 * -1 (-1r2) + -4r + -4 = -8 Reorder the terms: -4 + -4r + (-1r2) = -8 Solving -4 + -4r + (-1r2) = -8 Solving for variable 'r'. Reorder the terms: -4 + 8 + -4r + (-1r2) = -8 + 8 Combine like terms: -4 + 8 = 4 4 + -4r + (-1r2) = -8 + 8 Combine like terms: -8 + 8 = 0 4 + -4r + (-1r2) = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 4r + r2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + 4r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4r + r2 = 0 + 4 4r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 4r + r2 = 4 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 = 4 + 4 Reorder the terms: 4 + 4r + r2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4r + r2 = 8 Factor a perfect square on the left side: ((r) + 2)((r) + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting ((r) + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
(r) + 2 = 2.828427125 Simplifying (r) + 2 = 2.828427125 r + 2 = 2.828427125 Reorder the terms: 2 + r = 2.828427125 Solving 2 + r = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + r = 2.828427125 + -2 r = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 r = 0.828427125 Simplifying r = 0.828427125Subproblem 2
(r) + 2 = -2.828427125 Simplifying (r) + 2 = -2.828427125 r + 2 = -2.828427125 Reorder the terms: 2 + r = -2.828427125 Solving 2 + r = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + r = -2.828427125 + -2 r = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 r = -4.828427125 Simplifying r = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.828427125, -4.828427125}
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