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Simplifying x2 + -25407x + 45890000 = 0 Reorder the terms: 45890000 + -25407x + x2 = 0 Solving 45890000 + -25407x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45890000' to each side of the equation. 45890000 + -25407x + -45890000 + x2 = 0 + -45890000 Reorder the terms: 45890000 + -45890000 + -25407x + x2 = 0 + -45890000 Combine like terms: 45890000 + -45890000 = 0 0 + -25407x + x2 = 0 + -45890000 -25407x + x2 = 0 + -45890000 Combine like terms: 0 + -45890000 = -45890000 -25407x + x2 = -45890000 The x term is -25407x. Take half its coefficient (-12703.5). Square it (161378912.3) and add it to both sides. Add '161378912.3' to each side of the equation. -25407x + 161378912.3 + x2 = -45890000 + 161378912.3 Reorder the terms: 161378912.3 + -25407x + x2 = -45890000 + 161378912.3 Combine like terms: -45890000 + 161378912.3 = 115488912.3 161378912.3 + -25407x + x2 = 115488912.3 Factor a perfect square on the left side: (x + -12703.5)(x + -12703.5) = 115488912.3 Calculate the square root of the right side: 10746.576771233 Break this problem into two subproblems by setting (x + -12703.5) equal to 10746.576771233 and -10746.576771233.Subproblem 1
x + -12703.5 = 10746.576771233 Simplifying x + -12703.5 = 10746.576771233 Reorder the terms: -12703.5 + x = 10746.576771233 Solving -12703.5 + x = 10746.576771233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12703.5' to each side of the equation. -12703.5 + 12703.5 + x = 10746.576771233 + 12703.5 Combine like terms: -12703.5 + 12703.5 = 0.0 0.0 + x = 10746.576771233 + 12703.5 x = 10746.576771233 + 12703.5 Combine like terms: 10746.576771233 + 12703.5 = 23450.076771233 x = 23450.076771233 Simplifying x = 23450.076771233Subproblem 2
x + -12703.5 = -10746.576771233 Simplifying x + -12703.5 = -10746.576771233 Reorder the terms: -12703.5 + x = -10746.576771233 Solving -12703.5 + x = -10746.576771233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12703.5' to each side of the equation. -12703.5 + 12703.5 + x = -10746.576771233 + 12703.5 Combine like terms: -12703.5 + 12703.5 = 0.0 0.0 + x = -10746.576771233 + 12703.5 x = -10746.576771233 + 12703.5 Combine like terms: -10746.576771233 + 12703.5 = 1956.923228767 x = 1956.923228767 Simplifying x = 1956.923228767Solution
The solution to the problem is based on the solutions from the subproblems. x = {23450.076771233, 1956.923228767}
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