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Simplifying x4 + -10500x2 + 1250000 = 0 Reorder the terms: 1250000 + -10500x2 + x4 = 0 Solving 1250000 + -10500x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1250000' to each side of the equation. 1250000 + -10500x2 + -1250000 + x4 = 0 + -1250000 Reorder the terms: 1250000 + -1250000 + -10500x2 + x4 = 0 + -1250000 Combine like terms: 1250000 + -1250000 = 0 0 + -10500x2 + x4 = 0 + -1250000 -10500x2 + x4 = 0 + -1250000 Combine like terms: 0 + -1250000 = -1250000 -10500x2 + x4 = -1250000 The x term is -10500x2. Take half its coefficient (-5250). Square it (27562500) and add it to both sides. Add '27562500' to each side of the equation. -10500x2 + 27562500 + x4 = -1250000 + 27562500 Reorder the terms: 27562500 + -10500x2 + x4 = -1250000 + 27562500 Combine like terms: -1250000 + 27562500 = 26312500 27562500 + -10500x2 + x4 = 26312500 Factor a perfect square on the left side: (x2 + -5250)(x2 + -5250) = 26312500 Calculate the square root of the right side: 5129.571132171 Break this problem into two subproblems by setting (x2 + -5250) equal to 5129.571132171 and -5129.571132171.Subproblem 1
x2 + -5250 = 5129.571132171 Simplifying x2 + -5250 = 5129.571132171 Reorder the terms: -5250 + x2 = 5129.571132171 Solving -5250 + x2 = 5129.571132171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5250' to each side of the equation. -5250 + 5250 + x2 = 5129.571132171 + 5250 Combine like terms: -5250 + 5250 = 0 0 + x2 = 5129.571132171 + 5250 x2 = 5129.571132171 + 5250 Combine like terms: 5129.571132171 + 5250 = 10379.571132171 x2 = 10379.571132171 Simplifying x2 = 10379.571132171 Take the square root of each side: x = {-101.880180272, 101.880180272}Subproblem 2
x2 + -5250 = -5129.571132171 Simplifying x2 + -5250 = -5129.571132171 Reorder the terms: -5250 + x2 = -5129.571132171 Solving -5250 + x2 = -5129.571132171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5250' to each side of the equation. -5250 + 5250 + x2 = -5129.571132171 + 5250 Combine like terms: -5250 + 5250 = 0 0 + x2 = -5129.571132171 + 5250 x2 = -5129.571132171 + 5250 Combine like terms: -5129.571132171 + 5250 = 120.428867829 x2 = 120.428867829 Simplifying x2 = 120.428867829 Take the square root of each side: x = {-10.97400874, 10.97400874}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-101.880180272, 101.880180272, -10.97400874, 10.97400874}
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