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Simplifying 0 = 2.4x2 + 90.8x + 1.59 Reorder the terms: 0 = 1.59 + 90.8x + 2.4x2 Solving 0 = 1.59 + 90.8x + 2.4x2 Solving for variable 'x'. Combine like terms: 0 + -1.59 = -1.59 -1.59 + -90.8x + -2.4x2 = 1.59 + 90.8x + 2.4x2 + -1.59 + -90.8x + -2.4x2 Reorder the terms: -1.59 + -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 -1.59 + -90.8x + -2.4x2 = 0.00 + 90.8x + -90.8x + 2.4x2 + -2.4x2 -1.59 + -90.8x + -2.4x2 = 90.8x + -90.8x + 2.4x2 + -2.4x2 Combine like terms: 90.8x + -90.8x = 0.0 -1.59 + -90.8x + -2.4x2 = 0.0 + 2.4x2 + -2.4x2 -1.59 + -90.8x + -2.4x2 = 2.4x2 + -2.4x2 Combine like terms: 2.4x2 + -2.4x2 = 0.0 -1.59 + -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'. 0.6625 + 37.83333333x + x2 = 0 Move the constant term to the right: Add '-0.6625' to each side of the equation. 0.6625 + 37.83333333x + -0.6625 + x2 = 0 + -0.6625 Reorder the terms: 0.6625 + -0.6625 + 37.83333333x + x2 = 0 + -0.6625 Combine like terms: 0.6625 + -0.6625 = 0.0000 0.0000 + 37.83333333x + x2 = 0 + -0.6625 37.83333333x + x2 = 0 + -0.6625 Combine like terms: 0 + -0.6625 = -0.6625 37.83333333x + x2 = -0.6625 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 = -0.6625 + 357.8402779 Reorder the terms: 357.8402779 + 37.83333333x + x2 = -0.6625 + 357.8402779 Combine like terms: -0.6625 + 357.8402779 = 357.1777779 357.8402779 + 37.83333333x + x2 = 357.1777779 Factor a perfect square on the left side: (x + 18.91666667)(x + 18.91666667) = 357.1777779 Calculate the square root of the right side: 18.899147544 Break this problem into two subproblems by setting (x + 18.91666667) equal to 18.899147544 and -18.899147544.Subproblem 1
x + 18.91666667 = 18.899147544 Simplifying x + 18.91666667 = 18.899147544 Reorder the terms: 18.91666667 + x = 18.899147544 Solving 18.91666667 + x = 18.899147544 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 = 18.899147544 + -18.91666667 Combine like terms: 18.91666667 + -18.91666667 = 0.00000000 0.00000000 + x = 18.899147544 + -18.91666667 x = 18.899147544 + -18.91666667 Combine like terms: 18.899147544 + -18.91666667 = -0.017519126 x = -0.017519126 Simplifying x = -0.017519126Subproblem 2
x + 18.91666667 = -18.899147544 Simplifying x + 18.91666667 = -18.899147544 Reorder the terms: 18.91666667 + x = -18.899147544 Solving 18.91666667 + x = -18.899147544 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 = -18.899147544 + -18.91666667 Combine like terms: 18.91666667 + -18.91666667 = 0.00000000 0.00000000 + x = -18.899147544 + -18.91666667 x = -18.899147544 + -18.91666667 Combine like terms: -18.899147544 + -18.91666667 = -37.815814214 x = -37.815814214 Simplifying x = -37.815814214Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.017519126, -37.815814214}
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