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Simplifying 20x4 + -18x2 = 11 Reorder the terms: -18x2 + 20x4 = 11 Solving -18x2 + 20x4 = 11 Solving for variable 'x'. Reorder the terms: -11 + -18x2 + 20x4 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -18x2 + 20x4 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.55 + -0.9x2 + x4 = 0 Move the constant term to the right: Add '0.55' to each side of the equation. -0.55 + -0.9x2 + 0.55 + x4 = 0 + 0.55 Reorder the terms: -0.55 + 0.55 + -0.9x2 + x4 = 0 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + -0.9x2 + x4 = 0 + 0.55 -0.9x2 + x4 = 0 + 0.55 Combine like terms: 0 + 0.55 = 0.55 -0.9x2 + x4 = 0.55 The x term is -0.9x2. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x2 + 0.2025 + x4 = 0.55 + 0.2025 Reorder the terms: 0.2025 + -0.9x2 + x4 = 0.55 + 0.2025 Combine like terms: 0.55 + 0.2025 = 0.7525 0.2025 + -0.9x2 + x4 = 0.7525 Factor a perfect square on the left side: (x2 + -0.45)(x2 + -0.45) = 0.7525 Calculate the square root of the right side: 0.867467579 Break this problem into two subproblems by setting (x2 + -0.45) equal to 0.867467579 and -0.867467579.Subproblem 1
x2 + -0.45 = 0.867467579 Simplifying x2 + -0.45 = 0.867467579 Reorder the terms: -0.45 + x2 = 0.867467579 Solving -0.45 + x2 = 0.867467579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x2 = 0.867467579 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x2 = 0.867467579 + 0.45 x2 = 0.867467579 + 0.45 Combine like terms: 0.867467579 + 0.45 = 1.317467579 x2 = 1.317467579 Simplifying x2 = 1.317467579 Take the square root of each side: x = {-1.147809905, 1.147809905}Subproblem 2
x2 + -0.45 = -0.867467579 Simplifying x2 + -0.45 = -0.867467579 Reorder the terms: -0.45 + x2 = -0.867467579 Solving -0.45 + x2 = -0.867467579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x2 = -0.867467579 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x2 = -0.867467579 + 0.45 x2 = -0.867467579 + 0.45 Combine like terms: -0.867467579 + 0.45 = -0.417467579 x2 = -0.417467579 Simplifying x2 = -0.417467579 Reorder the terms: 0.417467579 + x2 = -0.417467579 + 0.417467579 Combine like terms: -0.417467579 + 0.417467579 = 0.000000000 0.417467579 + x2 = 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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