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Simplifying 5x4 + -4x2 + -45 = 0 Reorder the terms: -45 + -4x2 + 5x4 = 0 Solving -45 + -4x2 + 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'. -9 + -0.8x2 + x4 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.8x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + -0.8x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.8x2 + x4 = 0 + 9 -0.8x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.8x2 + x4 = 9 The x term is -0.8x2. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x2 + 0.16 + x4 = 9 + 0.16 Reorder the terms: 0.16 + -0.8x2 + x4 = 9 + 0.16 Combine like terms: 9 + 0.16 = 9.16 0.16 + -0.8x2 + x4 = 9.16 Factor a perfect square on the left side: (x2 + -0.4)(x2 + -0.4) = 9.16 Calculate the square root of the right side: 3.02654919 Break this problem into two subproblems by setting (x2 + -0.4) equal to 3.02654919 and -3.02654919.Subproblem 1
x2 + -0.4 = 3.02654919 Simplifying x2 + -0.4 = 3.02654919 Reorder the terms: -0.4 + x2 = 3.02654919 Solving -0.4 + x2 = 3.02654919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x2 = 3.02654919 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x2 = 3.02654919 + 0.4 x2 = 3.02654919 + 0.4 Combine like terms: 3.02654919 + 0.4 = 3.42654919 x2 = 3.42654919 Simplifying x2 = 3.42654919 Take the square root of each side: x = {-1.851094052, 1.851094052}Subproblem 2
x2 + -0.4 = -3.02654919 Simplifying x2 + -0.4 = -3.02654919 Reorder the terms: -0.4 + x2 = -3.02654919 Solving -0.4 + x2 = -3.02654919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x2 = -3.02654919 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x2 = -3.02654919 + 0.4 x2 = -3.02654919 + 0.4 Combine like terms: -3.02654919 + 0.4 = -2.62654919 x2 = -2.62654919 Simplifying x2 = -2.62654919 Reorder the terms: 2.62654919 + x2 = -2.62654919 + 2.62654919 Combine like terms: -2.62654919 + 2.62654919 = 0.00000000 2.62654919 + x2 = 0.00000000 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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