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Simplifying 3x2 + -200x + 174 = 0 Reorder the terms: 174 + -200x + 3x2 = 0 Solving 174 + -200x + 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'. 58 + -66.66666667x + x2 = 0 Move the constant term to the right: Add '-58' to each side of the equation. 58 + -66.66666667x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -66.66666667x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -66.66666667x + x2 = 0 + -58 -66.66666667x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -66.66666667x + x2 = -58 The x term is -66.66666667x. Take half its coefficient (-33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. -66.66666667x + 1111.111112 + x2 = -58 + 1111.111112 Reorder the terms: 1111.111112 + -66.66666667x + x2 = -58 + 1111.111112 Combine like terms: -58 + 1111.111112 = 1053.111112 1111.111112 + -66.66666667x + x2 = 1053.111112 Factor a perfect square on the left side: (x + -33.33333334)(x + -33.33333334) = 1053.111112 Calculate the square root of the right side: 32.451673485 Break this problem into two subproblems by setting (x + -33.33333334) equal to 32.451673485 and -32.451673485.Subproblem 1
x + -33.33333334 = 32.451673485 Simplifying x + -33.33333334 = 32.451673485 Reorder the terms: -33.33333334 + x = 32.451673485 Solving -33.33333334 + x = 32.451673485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = 32.451673485 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = 32.451673485 + 33.33333334 x = 32.451673485 + 33.33333334 Combine like terms: 32.451673485 + 33.33333334 = 65.785006825 x = 65.785006825 Simplifying x = 65.785006825Subproblem 2
x + -33.33333334 = -32.451673485 Simplifying x + -33.33333334 = -32.451673485 Reorder the terms: -33.33333334 + x = -32.451673485 Solving -33.33333334 + x = -32.451673485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = -32.451673485 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = -32.451673485 + 33.33333334 x = -32.451673485 + 33.33333334 Combine like terms: -32.451673485 + 33.33333334 = 0.881659855 x = 0.881659855 Simplifying x = 0.881659855Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.785006825, 0.881659855}
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