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Simplifying 435 = X + (X + 25) * 3X Reorder the terms: 435 = X + (25 + X) * 3X Reorder the terms for easier multiplication: 435 = X + 3X(25 + X) 435 = X + (25 * 3X + X * 3X) 435 = X + (75X + 3X2) Combine like terms: X + 75X = 76X 435 = 76X + 3X2 Solving 435 = 76X + 3X2 Solving for variable 'X'. Reorder the terms: 435 + -76X + -3X2 = 76X + -76X + 3X2 + -3X2 Combine like terms: 76X + -76X = 0 435 + -76X + -3X2 = 0 + 3X2 + -3X2 435 + -76X + -3X2 = 3X2 + -3X2 Combine like terms: 3X2 + -3X2 = 0 435 + -76X + -3X2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -145 + 25.33333333X + X2 = 0 Move the constant term to the right: Add '145' to each side of the equation. -145 + 25.33333333X + 145 + X2 = 0 + 145 Reorder the terms: -145 + 145 + 25.33333333X + X2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + 25.33333333X + X2 = 0 + 145 25.33333333X + X2 = 0 + 145 Combine like terms: 0 + 145 = 145 25.33333333X + X2 = 145 The X term is 25.33333333X. Take half its coefficient (12.66666667). Square it (160.4444445) and add it to both sides. Add '160.4444445' to each side of the equation. 25.33333333X + 160.4444445 + X2 = 145 + 160.4444445 Reorder the terms: 160.4444445 + 25.33333333X + X2 = 145 + 160.4444445 Combine like terms: 145 + 160.4444445 = 305.4444445 160.4444445 + 25.33333333X + X2 = 305.4444445 Factor a perfect square on the left side: (X + 12.66666667)(X + 12.66666667) = 305.4444445 Calculate the square root of the right side: 17.476968973 Break this problem into two subproblems by setting (X + 12.66666667) equal to 17.476968973 and -17.476968973.Subproblem 1
X + 12.66666667 = 17.476968973 Simplifying X + 12.66666667 = 17.476968973 Reorder the terms: 12.66666667 + X = 17.476968973 Solving 12.66666667 + X = 17.476968973 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-12.66666667' to each side of the equation. 12.66666667 + -12.66666667 + X = 17.476968973 + -12.66666667 Combine like terms: 12.66666667 + -12.66666667 = 0.00000000 0.00000000 + X = 17.476968973 + -12.66666667 X = 17.476968973 + -12.66666667 Combine like terms: 17.476968973 + -12.66666667 = 4.810302303 X = 4.810302303 Simplifying X = 4.810302303Subproblem 2
X + 12.66666667 = -17.476968973 Simplifying X + 12.66666667 = -17.476968973 Reorder the terms: 12.66666667 + X = -17.476968973 Solving 12.66666667 + X = -17.476968973 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-12.66666667' to each side of the equation. 12.66666667 + -12.66666667 + X = -17.476968973 + -12.66666667 Combine like terms: 12.66666667 + -12.66666667 = 0.00000000 0.00000000 + X = -17.476968973 + -12.66666667 X = -17.476968973 + -12.66666667 Combine like terms: -17.476968973 + -12.66666667 = -30.143635643 X = -30.143635643 Simplifying X = -30.143635643Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.810302303, -30.143635643}
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