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Simplifying 747 = -2.4x2 + 90.8x + 1.59 Reorder the terms: 747 = 1.59 + 90.8x + -2.4x2 Solving 747 = 1.59 + 90.8x + -2.4x2 Solving for variable 'x'. Combine like terms: 747 + -1.59 = 745.41 745.41 + -90.8x + 2.4x2 = 1.59 + 90.8x + -2.4x2 + -1.59 + -90.8x + 2.4x2 Reorder the terms: 745.41 + -90.8x + 2.4x2 = 1.59 + -1.59 + 90.8x + -90.8x + -2.4x2 + 2.4x2 Combine like terms: 1.59 + -1.59 = 0.00 745.41 + -90.8x + 2.4x2 = 0.00 + 90.8x + -90.8x + -2.4x2 + 2.4x2 745.41 + -90.8x + 2.4x2 = 90.8x + -90.8x + -2.4x2 + 2.4x2 Combine like terms: 90.8x + -90.8x = 0.0 745.41 + -90.8x + 2.4x2 = 0.0 + -2.4x2 + 2.4x2 745.41 + -90.8x + 2.4x2 = -2.4x2 + 2.4x2 Combine like terms: -2.4x2 + 2.4x2 = 0.0 745.41 + -90.8x + 2.4x2 = 0.0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. 310.5875 + -37.83333333x + x2 = 0 Move the constant term to the right: Add '-310.5875' to each side of the equation. 310.5875 + -37.83333333x + -310.5875 + x2 = 0 + -310.5875 Reorder the terms: 310.5875 + -310.5875 + -37.83333333x + x2 = 0 + -310.5875 Combine like terms: 310.5875 + -310.5875 = 0.0000 0.0000 + -37.83333333x + x2 = 0 + -310.5875 -37.83333333x + x2 = 0 + -310.5875 Combine like terms: 0 + -310.5875 = -310.5875 -37.83333333x + x2 = -310.5875 The x term is -37.83333333x. Take half its coefficient (-18.91666667). Square it (357.8402779) and add it to both sides. Add '357.8402779' to each side of the equation. -37.83333333x + 357.8402779 + x2 = -310.5875 + 357.8402779 Reorder the terms: 357.8402779 + -37.83333333x + x2 = -310.5875 + 357.8402779 Combine like terms: -310.5875 + 357.8402779 = 47.2527779 357.8402779 + -37.83333333x + x2 = 47.2527779 Factor a perfect square on the left side: (x + -18.91666667)(x + -18.91666667) = 47.2527779 Calculate the square root of the right side: 6.874065602 Break this problem into two subproblems by setting (x + -18.91666667) equal to 6.874065602 and -6.874065602.Subproblem 1
x + -18.91666667 = 6.874065602 Simplifying x + -18.91666667 = 6.874065602 Reorder the terms: -18.91666667 + x = 6.874065602 Solving -18.91666667 + x = 6.874065602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.91666667' to each side of the equation. -18.91666667 + 18.91666667 + x = 6.874065602 + 18.91666667 Combine like terms: -18.91666667 + 18.91666667 = 0.00000000 0.00000000 + x = 6.874065602 + 18.91666667 x = 6.874065602 + 18.91666667 Combine like terms: 6.874065602 + 18.91666667 = 25.790732272 x = 25.790732272 Simplifying x = 25.790732272Subproblem 2
x + -18.91666667 = -6.874065602 Simplifying x + -18.91666667 = -6.874065602 Reorder the terms: -18.91666667 + x = -6.874065602 Solving -18.91666667 + x = -6.874065602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.91666667' to each side of the equation. -18.91666667 + 18.91666667 + x = -6.874065602 + 18.91666667 Combine like terms: -18.91666667 + 18.91666667 = 0.00000000 0.00000000 + x = -6.874065602 + 18.91666667 x = -6.874065602 + 18.91666667 Combine like terms: -6.874065602 + 18.91666667 = 12.042601068 x = 12.042601068 Simplifying x = 12.042601068Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.790732272, 12.042601068}
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