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Simplifying 45x4 + 1750x2 + -4125 = 0 Reorder the terms: -4125 + 1750x2 + 45x4 = 0 Solving -4125 + 1750x2 + 45x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-825 + 350x2 + 9x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-825 + 350x2 + 9x4)' equal to zero and attempt to solve: Simplifying -825 + 350x2 + 9x4 = 0 Solving -825 + 350x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -91.66666667 + 38.88888889x2 + x4 = 0 Move the constant term to the right: Add '91.66666667' to each side of the equation. -91.66666667 + 38.88888889x2 + 91.66666667 + x4 = 0 + 91.66666667 Reorder the terms: -91.66666667 + 91.66666667 + 38.88888889x2 + x4 = 0 + 91.66666667 Combine like terms: -91.66666667 + 91.66666667 = 0.00000000 0.00000000 + 38.88888889x2 + x4 = 0 + 91.66666667 38.88888889x2 + x4 = 0 + 91.66666667 Combine like terms: 0 + 91.66666667 = 91.66666667 38.88888889x2 + x4 = 91.66666667 The x term is 38.88888889x2. Take half its coefficient (19.44444445). Square it (378.0864200) and add it to both sides. Add '378.0864200' to each side of the equation. 38.88888889x2 + 378.0864200 + x4 = 91.66666667 + 378.0864200 Reorder the terms: 378.0864200 + 38.88888889x2 + x4 = 91.66666667 + 378.0864200 Combine like terms: 91.66666667 + 378.0864200 = 469.75308667 378.0864200 + 38.88888889x2 + x4 = 469.75308667 Factor a perfect square on the left side: (x2 + 19.44444445)(x2 + 19.44444445) = 469.75308667 Calculate the square root of the right side: 21.673788009 Break this problem into two subproblems by setting (x2 + 19.44444445) equal to 21.673788009 and -21.673788009.Subproblem 1
x2 + 19.44444445 = 21.673788009 Simplifying x2 + 19.44444445 = 21.673788009 Reorder the terms: 19.44444445 + x2 = 21.673788009 Solving 19.44444445 + x2 = 21.673788009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.44444445' to each side of the equation. 19.44444445 + -19.44444445 + x2 = 21.673788009 + -19.44444445 Combine like terms: 19.44444445 + -19.44444445 = 0.00000000 0.00000000 + x2 = 21.673788009 + -19.44444445 x2 = 21.673788009 + -19.44444445 Combine like terms: 21.673788009 + -19.44444445 = 2.229343559 x2 = 2.229343559 Simplifying x2 = 2.229343559 Take the square root of each side: x = {-1.493098643, 1.493098643}Subproblem 2
x2 + 19.44444445 = -21.673788009 Simplifying x2 + 19.44444445 = -21.673788009 Reorder the terms: 19.44444445 + x2 = -21.673788009 Solving 19.44444445 + x2 = -21.673788009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.44444445' to each side of the equation. 19.44444445 + -19.44444445 + x2 = -21.673788009 + -19.44444445 Combine like terms: 19.44444445 + -19.44444445 = 0.00000000 0.00000000 + x2 = -21.673788009 + -19.44444445 x2 = -21.673788009 + -19.44444445 Combine like terms: -21.673788009 + -19.44444445 = -41.118232459 x2 = -41.118232459 Simplifying x2 = -41.118232459 Reorder the terms: 41.118232459 + x2 = -41.118232459 + 41.118232459 Combine like terms: -41.118232459 + 41.118232459 = 0.000000000 41.118232459 + 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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