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Simplifying 5x4 + -9x2 + -4 = 0 Reorder the terms: -4 + -9x2 + 5x4 = 0 Solving -4 + -9x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -1.8x2 + x4 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.8x2 + 0.8 + x4 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.8x2 + x4 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.8x2 + x4 = 0 + 0.8 -1.8x2 + x4 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.8x2 + x4 = 0.8 The x term is -1.8x2. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x2 + 0.81 + x4 = 0.8 + 0.81 Reorder the terms: 0.81 + -1.8x2 + x4 = 0.8 + 0.81 Combine like terms: 0.8 + 0.81 = 1.61 0.81 + -1.8x2 + x4 = 1.61 Factor a perfect square on the left side: (x2 + -0.9)(x2 + -0.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x2 + -0.9) equal to 1.268857754 and -1.268857754.Subproblem 1
x2 + -0.9 = 1.268857754 Simplifying x2 + -0.9 = 1.268857754 Reorder the terms: -0.9 + x2 = 1.268857754 Solving -0.9 + x2 = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x2 = 1.268857754 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x2 = 1.268857754 + 0.9 x2 = 1.268857754 + 0.9 Combine like terms: 1.268857754 + 0.9 = 2.168857754 x2 = 2.168857754 Simplifying x2 = 2.168857754 Take the square root of each side: x = {-1.472704232, 1.472704232}Subproblem 2
x2 + -0.9 = -1.268857754 Simplifying x2 + -0.9 = -1.268857754 Reorder the terms: -0.9 + x2 = -1.268857754 Solving -0.9 + x2 = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x2 = -1.268857754 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x2 = -1.268857754 + 0.9 x2 = -1.268857754 + 0.9 Combine like terms: -1.268857754 + 0.9 = -0.368857754 x2 = -0.368857754 Simplifying x2 = -0.368857754 Reorder the terms: 0.368857754 + x2 = -0.368857754 + 0.368857754 Combine like terms: -0.368857754 + 0.368857754 = 0.000000000 0.368857754 + 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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