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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 = 668.4277779 357.8402779 + 37.83333333x + x2 = 668.4277779 Factor a perfect square on the left side: (x + 18.91666667)(x + 18.91666667) = 668.4277779 Calculate the square root of the right side: 25.853970254 Break this problem into two subproblems by setting (x + 18.91666667) equal to 25.853970254 and -25.853970254.Subproblem 1
x + 18.91666667 = 25.853970254 Simplifying x + 18.91666667 = 25.853970254 Reorder the terms: 18.91666667 + x = 25.853970254 Solving 18.91666667 + x = 25.853970254 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 = 25.853970254 + -18.91666667 Combine like terms: 18.91666667 + -18.91666667 = 0.00000000 0.00000000 + x = 25.853970254 + -18.91666667 x = 25.853970254 + -18.91666667 Combine like terms: 25.853970254 + -18.91666667 = 6.937303584 x = 6.937303584 Simplifying x = 6.937303584Subproblem 2
x + 18.91666667 = -25.853970254 Simplifying x + 18.91666667 = -25.853970254 Reorder the terms: 18.91666667 + x = -25.853970254 Solving 18.91666667 + x = -25.853970254 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 = -25.853970254 + -18.91666667 Combine like terms: 18.91666667 + -18.91666667 = 0.00000000 0.00000000 + x = -25.853970254 + -18.91666667 x = -25.853970254 + -18.91666667 Combine like terms: -25.853970254 + -18.91666667 = -44.770636924 x = -44.770636924 Simplifying x = -44.770636924Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.937303584, -44.770636924}
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