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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 = 14652.85608 20807.31621 + -288.4948263x2 + x4 = 14652.85608 Factor a perfect square on the left side: (x2 + -144.2474132)(x2 + -144.2474132) = 14652.85608 Calculate the square root of the right side: 121.048982152 Break this problem into two subproblems by setting (x2 + -144.2474132) equal to 121.048982152 and -121.048982152.Subproblem 1
x2 + -144.2474132 = 121.048982152 Simplifying x2 + -144.2474132 = 121.048982152 Reorder the terms: -144.2474132 + x2 = 121.048982152 Solving -144.2474132 + x2 = 121.048982152 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 = 121.048982152 + 144.2474132 Combine like terms: -144.2474132 + 144.2474132 = 0.0000000 0.0000000 + x2 = 121.048982152 + 144.2474132 x2 = 121.048982152 + 144.2474132 Combine like terms: 121.048982152 + 144.2474132 = 265.296395352 x2 = 265.296395352 Simplifying x2 = 265.296395352 Take the square root of each side: x = {-16.287921763, 16.287921763}Subproblem 2
x2 + -144.2474132 = -121.048982152 Simplifying x2 + -144.2474132 = -121.048982152 Reorder the terms: -144.2474132 + x2 = -121.048982152 Solving -144.2474132 + x2 = -121.048982152 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 = -121.048982152 + 144.2474132 Combine like terms: -144.2474132 + 144.2474132 = 0.0000000 0.0000000 + x2 = -121.048982152 + 144.2474132 x2 = -121.048982152 + 144.2474132 Combine like terms: -121.048982152 + 144.2474132 = 23.198431048 x2 = 23.198431048 Simplifying x2 = 23.198431048 Take the square root of each side: x = {-4.816474961, 4.816474961}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.287921763, 16.287921763, -4.816474961, 4.816474961}
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