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Simplifying 5r4 + 10r2 + 2 = 0 Reorder the terms: 2 + 10r2 + 5r4 = 0 Solving 2 + 10r2 + 5r4 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 2r2 + r4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2r2 + -0.4 + r4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2r2 + r4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2r2 + r4 = 0 + -0.4 2r2 + r4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2r2 + r4 = -0.4 The r term is 2r2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r2 + 1 + r4 = -0.4 + 1 Reorder the terms: 1 + 2r2 + r4 = -0.4 + 1 Combine like terms: -0.4 + 1 = 0.6 1 + 2r2 + r4 = 0.6 Factor a perfect square on the left side: (r2 + 1)(r2 + 1) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (r2 + 1) equal to 0.774596669 and -0.774596669.Subproblem 1
r2 + 1 = 0.774596669 Simplifying r2 + 1 = 0.774596669 Reorder the terms: 1 + r2 = 0.774596669 Solving 1 + r2 = 0.774596669 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r2 = 0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + r2 = 0.774596669 + -1 r2 = 0.774596669 + -1 Combine like terms: 0.774596669 + -1 = -0.225403331 r2 = -0.225403331 Simplifying r2 = -0.225403331 Reorder the terms: 0.225403331 + r2 = -0.225403331 + 0.225403331 Combine like terms: -0.225403331 + 0.225403331 = 0.000000000 0.225403331 + r2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
r2 + 1 = -0.774596669 Simplifying r2 + 1 = -0.774596669 Reorder the terms: 1 + r2 = -0.774596669 Solving 1 + r2 = -0.774596669 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r2 = -0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + r2 = -0.774596669 + -1 r2 = -0.774596669 + -1 Combine like terms: -0.774596669 + -1 = -1.774596669 r2 = -1.774596669 Simplifying r2 = -1.774596669 Reorder the terms: 1.774596669 + r2 = -1.774596669 + 1.774596669 Combine like terms: -1.774596669 + 1.774596669 = 0.000000000 1.774596669 + r2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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