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Simplifying 0.753x2 + 451.8x + -265200 = 0 Reorder the terms: -265200 + 451.8x + 0.753x2 = 0 Solving -265200 + 451.8x + 0.753x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.753 the coefficient of the squared term: Divide each side by '0.753'. -352191.2351 + 600x + x2 = 0 Move the constant term to the right: Add '352191.2351' to each side of the equation. -352191.2351 + 600x + 352191.2351 + x2 = 0 + 352191.2351 Reorder the terms: -352191.2351 + 352191.2351 + 600x + x2 = 0 + 352191.2351 Combine like terms: -352191.2351 + 352191.2351 = 0.0000 0.0000 + 600x + x2 = 0 + 352191.2351 600x + x2 = 0 + 352191.2351 Combine like terms: 0 + 352191.2351 = 352191.2351 600x + x2 = 352191.2351 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = 352191.2351 + 90000 Reorder the terms: 90000 + 600x + x2 = 352191.2351 + 90000 Combine like terms: 352191.2351 + 90000 = 442191.2351 90000 + 600x + x2 = 442191.2351 Factor a perfect square on the left side: (x + 300)(x + 300) = 442191.2351 Calculate the square root of the right side: 664.974612373 Break this problem into two subproblems by setting (x + 300) equal to 664.974612373 and -664.974612373.Subproblem 1
x + 300 = 664.974612373 Simplifying x + 300 = 664.974612373 Reorder the terms: 300 + x = 664.974612373 Solving 300 + x = 664.974612373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 664.974612373 + -300 Combine like terms: 300 + -300 = 0 0 + x = 664.974612373 + -300 x = 664.974612373 + -300 Combine like terms: 664.974612373 + -300 = 364.974612373 x = 364.974612373 Simplifying x = 364.974612373Subproblem 2
x + 300 = -664.974612373 Simplifying x + 300 = -664.974612373 Reorder the terms: 300 + x = -664.974612373 Solving 300 + x = -664.974612373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -664.974612373 + -300 Combine like terms: 300 + -300 = 0 0 + x = -664.974612373 + -300 x = -664.974612373 + -300 Combine like terms: -664.974612373 + -300 = -964.974612373 x = -964.974612373 Simplifying x = -964.974612373Solution
The solution to the problem is based on the solutions from the subproblems. x = {364.974612373, -964.974612373}
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