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Simplifying 259.97x4 + -75000x2 + -1599975 = 0 Reorder the terms: -1599975 + -75000x2 + 259.97x4 = 0 Solving -1599975 + -75000x2 + 259.97x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 259.97 the coefficient of the squared term: Divide each side by '259.97'. -6154.46013 + -288.4948263x2 + x4 = 0 Move the constant term to the right: Add '6154.46013' to each side of the equation. -6154.46013 + -288.4948263x2 + 6154.46013 + x4 = 0 + 6154.46013 Reorder the terms: -6154.46013 + 6154.46013 + -288.4948263x2 + x4 = 0 + 6154.46013 Combine like terms: -6154.46013 + 6154.46013 = 0.00000 0.00000 + -288.4948263x2 + x4 = 0 + 6154.46013 -288.4948263x2 + x4 = 0 + 6154.46013 Combine like terms: 0 + 6154.46013 = 6154.46013 -288.4948263x2 + x4 = 6154.46013 The x term is -288.4948263x2. Take half its coefficient (-144.2474132). Square it (20807.31621) and add it to both sides. Add '20807.31621' to each side of the equation. -288.4948263x2 + 20807.31621 + x4 = 6154.46013 + 20807.31621 Reorder the terms: 20807.31621 + -288.4948263x2 + x4 = 6154.46013 + 20807.31621 Combine like terms: 6154.46013 + 20807.31621 = 26961.77634 20807.31621 + -288.4948263x2 + x4 = 26961.77634 Factor a perfect square on the left side: (x2 + -144.2474132)(x2 + -144.2474132) = 26961.77634 Calculate the square root of the right side: 164.200415164 Break this problem into two subproblems by setting (x2 + -144.2474132) equal to 164.200415164 and -164.200415164.Subproblem 1
x2 + -144.2474132 = 164.200415164 Simplifying x2 + -144.2474132 = 164.200415164 Reorder the terms: -144.2474132 + x2 = 164.200415164 Solving -144.2474132 + x2 = 164.200415164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '144.2474132' to each side of the equation. -144.2474132 + 144.2474132 + x2 = 164.200415164 + 144.2474132 Combine like terms: -144.2474132 + 144.2474132 = 0.0000000 0.0000000 + x2 = 164.200415164 + 144.2474132 x2 = 164.200415164 + 144.2474132 Combine like terms: 164.200415164 + 144.2474132 = 308.447828364 x2 = 308.447828364 Simplifying x2 = 308.447828364 Take the square root of each side: x = {-17.562682835, 17.562682835}Subproblem 2
x2 + -144.2474132 = -164.200415164 Simplifying x2 + -144.2474132 = -164.200415164 Reorder the terms: -144.2474132 + x2 = -164.200415164 Solving -144.2474132 + x2 = -164.200415164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '144.2474132' to each side of the equation. -144.2474132 + 144.2474132 + x2 = -164.200415164 + 144.2474132 Combine like terms: -144.2474132 + 144.2474132 = 0.0000000 0.0000000 + x2 = -164.200415164 + 144.2474132 x2 = -164.200415164 + 144.2474132 Combine like terms: -164.200415164 + 144.2474132 = -19.953001964 x2 = -19.953001964 Simplifying x2 = -19.953001964 Reorder the terms: 19.953001964 + x2 = -19.953001964 + 19.953001964 Combine like terms: -19.953001964 + 19.953001964 = 0.000000000 19.953001964 + 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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