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Simplifying -2.03x2 + 78.48x + 743 = 0 Reorder the terms: 743 + 78.48x + -2.03x2 = 0 Solving 743 + 78.48x + -2.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.03 the coefficient of the squared term: Divide each side by '-2.03'. -366.0098522 + -38.66009852x + x2 = 0 Move the constant term to the right: Add '366.0098522' to each side of the equation. -366.0098522 + -38.66009852x + 366.0098522 + x2 = 0 + 366.0098522 Reorder the terms: -366.0098522 + 366.0098522 + -38.66009852x + x2 = 0 + 366.0098522 Combine like terms: -366.0098522 + 366.0098522 = 0.0000000 0.0000000 + -38.66009852x + x2 = 0 + 366.0098522 -38.66009852x + x2 = 0 + 366.0098522 Combine like terms: 0 + 366.0098522 = 366.0098522 -38.66009852x + x2 = 366.0098522 The x term is -38.66009852x. Take half its coefficient (-19.33004926). Square it (373.6508044) and add it to both sides. Add '373.6508044' to each side of the equation. -38.66009852x + 373.6508044 + x2 = 366.0098522 + 373.6508044 Reorder the terms: 373.6508044 + -38.66009852x + x2 = 366.0098522 + 373.6508044 Combine like terms: 366.0098522 + 373.6508044 = 739.6606566 373.6508044 + -38.66009852x + x2 = 739.6606566 Factor a perfect square on the left side: (x + -19.33004926)(x + -19.33004926) = 739.6606566 Calculate the square root of the right side: 27.196703047 Break this problem into two subproblems by setting (x + -19.33004926) equal to 27.196703047 and -27.196703047.Subproblem 1
x + -19.33004926 = 27.196703047 Simplifying x + -19.33004926 = 27.196703047 Reorder the terms: -19.33004926 + x = 27.196703047 Solving -19.33004926 + x = 27.196703047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.33004926' to each side of the equation. -19.33004926 + 19.33004926 + x = 27.196703047 + 19.33004926 Combine like terms: -19.33004926 + 19.33004926 = 0.00000000 0.00000000 + x = 27.196703047 + 19.33004926 x = 27.196703047 + 19.33004926 Combine like terms: 27.196703047 + 19.33004926 = 46.526752307 x = 46.526752307 Simplifying x = 46.526752307Subproblem 2
x + -19.33004926 = -27.196703047 Simplifying x + -19.33004926 = -27.196703047 Reorder the terms: -19.33004926 + x = -27.196703047 Solving -19.33004926 + x = -27.196703047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.33004926' to each side of the equation. -19.33004926 + 19.33004926 + x = -27.196703047 + 19.33004926 Combine like terms: -19.33004926 + 19.33004926 = 0.00000000 0.00000000 + x = -27.196703047 + 19.33004926 x = -27.196703047 + 19.33004926 Combine like terms: -27.196703047 + 19.33004926 = -7.866653787 x = -7.866653787 Simplifying x = -7.866653787Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.526752307, -7.866653787}
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