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Simplifying r4 + -2.12r2 + -2.89 = 0 Reorder the terms: -2.89 + -2.12r2 + r4 = 0 Solving -2.89 + -2.12r2 + r4 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '2.89' to each side of the equation. -2.89 + -2.12r2 + 2.89 + r4 = 0 + 2.89 Reorder the terms: -2.89 + 2.89 + -2.12r2 + r4 = 0 + 2.89 Combine like terms: -2.89 + 2.89 = 0.00 0.00 + -2.12r2 + r4 = 0 + 2.89 -2.12r2 + r4 = 0 + 2.89 Combine like terms: 0 + 2.89 = 2.89 -2.12r2 + r4 = 2.89 The r term is -2.12r2. Take half its coefficient (-1.06). Square it (1.1236) and add it to both sides. Add '1.1236' to each side of the equation. -2.12r2 + 1.1236 + r4 = 2.89 + 1.1236 Reorder the terms: 1.1236 + -2.12r2 + r4 = 2.89 + 1.1236 Combine like terms: 2.89 + 1.1236 = 4.0136 1.1236 + -2.12r2 + r4 = 4.0136 Factor a perfect square on the left side: (r2 + -1.06)(r2 + -1.06) = 4.0136 Calculate the square root of the right side: 2.003397115 Break this problem into two subproblems by setting (r2 + -1.06) equal to 2.003397115 and -2.003397115.Subproblem 1
r2 + -1.06 = 2.003397115 Simplifying r2 + -1.06 = 2.003397115 Reorder the terms: -1.06 + r2 = 2.003397115 Solving -1.06 + r2 = 2.003397115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.06' to each side of the equation. -1.06 + 1.06 + r2 = 2.003397115 + 1.06 Combine like terms: -1.06 + 1.06 = 0.00 0.00 + r2 = 2.003397115 + 1.06 r2 = 2.003397115 + 1.06 Combine like terms: 2.003397115 + 1.06 = 3.063397115 r2 = 3.063397115 Simplifying r2 = 3.063397115 Take the square root of each side: r = {-1.7502563, 1.7502563}Subproblem 2
r2 + -1.06 = -2.003397115 Simplifying r2 + -1.06 = -2.003397115 Reorder the terms: -1.06 + r2 = -2.003397115 Solving -1.06 + r2 = -2.003397115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.06' to each side of the equation. -1.06 + 1.06 + r2 = -2.003397115 + 1.06 Combine like terms: -1.06 + 1.06 = 0.00 0.00 + r2 = -2.003397115 + 1.06 r2 = -2.003397115 + 1.06 Combine like terms: -2.003397115 + 1.06 = -0.943397115 r2 = -0.943397115 Simplifying r2 = -0.943397115 Reorder the terms: 0.943397115 + r2 = -0.943397115 + 0.943397115 Combine like terms: -0.943397115 + 0.943397115 = 0.000000000 0.943397115 + 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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