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Simplifying 3x2 + 100x + -2600 = 0 Reorder the terms: -2600 + 100x + 3x2 = 0 Solving -2600 + 100x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -866.6666667 + 33.33333333x + x2 = 0 Move the constant term to the right: Add '866.6666667' to each side of the equation. -866.6666667 + 33.33333333x + 866.6666667 + x2 = 0 + 866.6666667 Reorder the terms: -866.6666667 + 866.6666667 + 33.33333333x + x2 = 0 + 866.6666667 Combine like terms: -866.6666667 + 866.6666667 = 0.0000000 0.0000000 + 33.33333333x + x2 = 0 + 866.6666667 33.33333333x + x2 = 0 + 866.6666667 Combine like terms: 0 + 866.6666667 = 866.6666667 33.33333333x + x2 = 866.6666667 The x term is 33.33333333x. Take half its coefficient (16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. 33.33333333x + 277.7777779 + x2 = 866.6666667 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333x + x2 = 866.6666667 + 277.7777779 Combine like terms: 866.6666667 + 277.7777779 = 1144.4444446 277.7777779 + 33.33333333x + x2 = 1144.4444446 Factor a perfect square on the left side: (x + 16.66666667)(x + 16.66666667) = 1144.4444446 Calculate the square root of the right side: 33.829638553 Break this problem into two subproblems by setting (x + 16.66666667) equal to 33.829638553 and -33.829638553.Subproblem 1
x + 16.66666667 = 33.829638553 Simplifying x + 16.66666667 = 33.829638553 Reorder the terms: 16.66666667 + x = 33.829638553 Solving 16.66666667 + x = 33.829638553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + x = 33.829638553 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = 33.829638553 + -16.66666667 x = 33.829638553 + -16.66666667 Combine like terms: 33.829638553 + -16.66666667 = 17.162971883 x = 17.162971883 Simplifying x = 17.162971883Subproblem 2
x + 16.66666667 = -33.829638553 Simplifying x + 16.66666667 = -33.829638553 Reorder the terms: 16.66666667 + x = -33.829638553 Solving 16.66666667 + x = -33.829638553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + x = -33.829638553 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = -33.829638553 + -16.66666667 x = -33.829638553 + -16.66666667 Combine like terms: -33.829638553 + -16.66666667 = -50.496305223 x = -50.496305223 Simplifying x = -50.496305223Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.162971883, -50.496305223}
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