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Simplifying 0.75x2 + 35x + -200 = 0 Reorder the terms: -200 + 35x + 0.75x2 = 0 Solving -200 + 35x + 0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. -266.6666667 + 46.66666667x + x2 = 0 Move the constant term to the right: Add '266.6666667' to each side of the equation. -266.6666667 + 46.66666667x + 266.6666667 + x2 = 0 + 266.6666667 Reorder the terms: -266.6666667 + 266.6666667 + 46.66666667x + x2 = 0 + 266.6666667 Combine like terms: -266.6666667 + 266.6666667 = 0.0000000 0.0000000 + 46.66666667x + x2 = 0 + 266.6666667 46.66666667x + x2 = 0 + 266.6666667 Combine like terms: 0 + 266.6666667 = 266.6666667 46.66666667x + x2 = 266.6666667 The x term is 46.66666667x. Take half its coefficient (23.33333334). Square it (544.4444448) and add it to both sides. Add '544.4444448' to each side of the equation. 46.66666667x + 544.4444448 + x2 = 266.6666667 + 544.4444448 Reorder the terms: 544.4444448 + 46.66666667x + x2 = 266.6666667 + 544.4444448 Combine like terms: 266.6666667 + 544.4444448 = 811.1111115 544.4444448 + 46.66666667x + x2 = 811.1111115 Factor a perfect square on the left side: (x + 23.33333334)(x + 23.33333334) = 811.1111115 Calculate the square root of the right side: 28.480012491 Break this problem into two subproblems by setting (x + 23.33333334) equal to 28.480012491 and -28.480012491.Subproblem 1
x + 23.33333334 = 28.480012491 Simplifying x + 23.33333334 = 28.480012491 Reorder the terms: 23.33333334 + x = 28.480012491 Solving 23.33333334 + x = 28.480012491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.33333334' to each side of the equation. 23.33333334 + -23.33333334 + x = 28.480012491 + -23.33333334 Combine like terms: 23.33333334 + -23.33333334 = 0.00000000 0.00000000 + x = 28.480012491 + -23.33333334 x = 28.480012491 + -23.33333334 Combine like terms: 28.480012491 + -23.33333334 = 5.146679151 x = 5.146679151 Simplifying x = 5.146679151Subproblem 2
x + 23.33333334 = -28.480012491 Simplifying x + 23.33333334 = -28.480012491 Reorder the terms: 23.33333334 + x = -28.480012491 Solving 23.33333334 + x = -28.480012491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.33333334' to each side of the equation. 23.33333334 + -23.33333334 + x = -28.480012491 + -23.33333334 Combine like terms: 23.33333334 + -23.33333334 = 0.00000000 0.00000000 + x = -28.480012491 + -23.33333334 x = -28.480012491 + -23.33333334 Combine like terms: -28.480012491 + -23.33333334 = -51.813345831 x = -51.813345831 Simplifying x = -51.813345831Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.146679151, -51.813345831}
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