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Simplifying 5x4 + 24x2 + 2 = 0 Reorder the terms: 2 + 24x2 + 5x4 = 0 Solving 2 + 24x2 + 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'. 0.4 + 4.8x2 + x4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 4.8x2 + -0.4 + x4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 4.8x2 + x4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 4.8x2 + x4 = 0 + -0.4 4.8x2 + x4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 4.8x2 + x4 = -0.4 The x term is 4.8x2. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x2 + 5.76 + x4 = -0.4 + 5.76 Reorder the terms: 5.76 + 4.8x2 + x4 = -0.4 + 5.76 Combine like terms: -0.4 + 5.76 = 5.36 5.76 + 4.8x2 + x4 = 5.36 Factor a perfect square on the left side: (x2 + 2.4)(x2 + 2.4) = 5.36 Calculate the square root of the right side: 2.315167381 Break this problem into two subproblems by setting (x2 + 2.4) equal to 2.315167381 and -2.315167381.Subproblem 1
x2 + 2.4 = 2.315167381 Simplifying x2 + 2.4 = 2.315167381 Reorder the terms: 2.4 + x2 = 2.315167381 Solving 2.4 + x2 = 2.315167381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x2 = 2.315167381 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x2 = 2.315167381 + -2.4 x2 = 2.315167381 + -2.4 Combine like terms: 2.315167381 + -2.4 = -0.084832619 x2 = -0.084832619 Simplifying x2 = -0.084832619 Reorder the terms: 0.084832619 + x2 = -0.084832619 + 0.084832619 Combine like terms: -0.084832619 + 0.084832619 = 0.000000000 0.084832619 + x2 = 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
x2 + 2.4 = -2.315167381 Simplifying x2 + 2.4 = -2.315167381 Reorder the terms: 2.4 + x2 = -2.315167381 Solving 2.4 + x2 = -2.315167381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x2 = -2.315167381 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x2 = -2.315167381 + -2.4 x2 = -2.315167381 + -2.4 Combine like terms: -2.315167381 + -2.4 = -4.715167381 x2 = -4.715167381 Simplifying x2 = -4.715167381 Reorder the terms: 4.715167381 + x2 = -4.715167381 + 4.715167381 Combine like terms: -4.715167381 + 4.715167381 = 0.000000000 4.715167381 + 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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