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Simplifying 0 = 2400 + -400x + -12x2 Solving 0 = 2400 + -400x + -12x2 Solving for variable 'x'. Combine like terms: 0 + -2400 = -2400 -2400 + 400x + 12x2 = 2400 + -400x + -12x2 + -2400 + 400x + 12x2 Reorder the terms: -2400 + 400x + 12x2 = 2400 + -2400 + -400x + 400x + -12x2 + 12x2 Combine like terms: 2400 + -2400 = 0 -2400 + 400x + 12x2 = 0 + -400x + 400x + -12x2 + 12x2 -2400 + 400x + 12x2 = -400x + 400x + -12x2 + 12x2 Combine like terms: -400x + 400x = 0 -2400 + 400x + 12x2 = 0 + -12x2 + 12x2 -2400 + 400x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -2400 + 400x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-600 + 100x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-600 + 100x + 3x2)' equal to zero and attempt to solve: Simplifying -600 + 100x + 3x2 = 0 Solving -600 + 100x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -200 + 33.33333333x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 33.33333333x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 33.33333333x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 33.33333333x + x2 = 0 + 200 33.33333333x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 33.33333333x + x2 = 200 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 = 200 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333x + x2 = 200 + 277.7777779 Combine like terms: 200 + 277.7777779 = 477.7777779 277.7777779 + 33.33333333x + x2 = 477.7777779 Factor a perfect square on the left side: (x + 16.66666667)(x + 16.66666667) = 477.7777779 Calculate the square root of the right side: 21.858128417 Break this problem into two subproblems by setting (x + 16.66666667) equal to 21.858128417 and -21.858128417.Subproblem 1
x + 16.66666667 = 21.858128417 Simplifying x + 16.66666667 = 21.858128417 Reorder the terms: 16.66666667 + x = 21.858128417 Solving 16.66666667 + x = 21.858128417 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 = 21.858128417 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = 21.858128417 + -16.66666667 x = 21.858128417 + -16.66666667 Combine like terms: 21.858128417 + -16.66666667 = 5.191461747 x = 5.191461747 Simplifying x = 5.191461747Subproblem 2
x + 16.66666667 = -21.858128417 Simplifying x + 16.66666667 = -21.858128417 Reorder the terms: 16.66666667 + x = -21.858128417 Solving 16.66666667 + x = -21.858128417 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 = -21.858128417 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = -21.858128417 + -16.66666667 x = -21.858128417 + -16.66666667 Combine like terms: -21.858128417 + -16.66666667 = -38.524795087 x = -38.524795087 Simplifying x = -38.524795087Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.191461747, -38.524795087}Solution
x = {5.191461747, -38.524795087}
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