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Simplifying -4x4 + -575x2 + -144 = 0 Reorder the terms: -144 + -575x2 + -4x4 = 0 Solving -144 + -575x2 + -4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(144 + 575x2 + 4x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(144 + 575x2 + 4x4)' equal to zero and attempt to solve: Simplifying 144 + 575x2 + 4x4 = 0 Solving 144 + 575x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 36 + 143.75x2 + x4 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + 143.75x2 + -36 + x4 = 0 + -36 Reorder the terms: 36 + -36 + 143.75x2 + x4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 143.75x2 + x4 = 0 + -36 143.75x2 + x4 = 0 + -36 Combine like terms: 0 + -36 = -36 143.75x2 + x4 = -36 The x term is 143.75x2. Take half its coefficient (71.875). Square it (5166.015625) and add it to both sides. Add '5166.015625' to each side of the equation. 143.75x2 + 5166.015625 + x4 = -36 + 5166.015625 Reorder the terms: 5166.015625 + 143.75x2 + x4 = -36 + 5166.015625 Combine like terms: -36 + 5166.015625 = 5130.015625 5166.015625 + 143.75x2 + x4 = 5130.015625 Factor a perfect square on the left side: (x2 + 71.875)(x2 + 71.875) = 5130.015625 Calculate the square root of the right side: 71.624127394 Break this problem into two subproblems by setting (x2 + 71.875) equal to 71.624127394 and -71.624127394.Subproblem 1
x2 + 71.875 = 71.624127394 Simplifying x2 + 71.875 = 71.624127394 Reorder the terms: 71.875 + x2 = 71.624127394 Solving 71.875 + x2 = 71.624127394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-71.875' to each side of the equation. 71.875 + -71.875 + x2 = 71.624127394 + -71.875 Combine like terms: 71.875 + -71.875 = 0.000 0.000 + x2 = 71.624127394 + -71.875 x2 = 71.624127394 + -71.875 Combine like terms: 71.624127394 + -71.875 = -0.250872606 x2 = -0.250872606 Simplifying x2 = -0.250872606 Reorder the terms: 0.250872606 + x2 = -0.250872606 + 0.250872606 Combine like terms: -0.250872606 + 0.250872606 = 0.000000000 0.250872606 + 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 + 71.875 = -71.624127394 Simplifying x2 + 71.875 = -71.624127394 Reorder the terms: 71.875 + x2 = -71.624127394 Solving 71.875 + x2 = -71.624127394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-71.875' to each side of the equation. 71.875 + -71.875 + x2 = -71.624127394 + -71.875 Combine like terms: 71.875 + -71.875 = 0.000 0.000 + x2 = -71.624127394 + -71.875 x2 = -71.624127394 + -71.875 Combine like terms: -71.624127394 + -71.875 = -143.499127394 x2 = -143.499127394 Simplifying x2 = -143.499127394 Reorder the terms: 143.499127394 + x2 = -143.499127394 + 143.499127394 Combine like terms: -143.499127394 + 143.499127394 = 0.000000000 143.499127394 + 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. 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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