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Simplifying 124.2 + -150.444x + 19.4028x2 = 0 Solving 124.2 + -150.444x + 19.4028x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.4028 the coefficient of the squared term: Divide each side by '19.4028'. 6.40113798 + -7.753726266x + x2 = 0 Move the constant term to the right: Add '-6.40113798' to each side of the equation. 6.40113798 + -7.753726266x + -6.40113798 + x2 = 0 + -6.40113798 Reorder the terms: 6.40113798 + -6.40113798 + -7.753726266x + x2 = 0 + -6.40113798 Combine like terms: 6.40113798 + -6.40113798 = 0.00000000 0.00000000 + -7.753726266x + x2 = 0 + -6.40113798 -7.753726266x + x2 = 0 + -6.40113798 Combine like terms: 0 + -6.40113798 = -6.40113798 -7.753726266x + x2 = -6.40113798 The x term is -7.753726266x. Take half its coefficient (-3.876863133). Square it (15.03006775) and add it to both sides. Add '15.03006775' to each side of the equation. -7.753726266x + 15.03006775 + x2 = -6.40113798 + 15.03006775 Reorder the terms: 15.03006775 + -7.753726266x + x2 = -6.40113798 + 15.03006775 Combine like terms: -6.40113798 + 15.03006775 = 8.62892977 15.03006775 + -7.753726266x + x2 = 8.62892977 Factor a perfect square on the left side: (x + -3.876863133)(x + -3.876863133) = 8.62892977 Calculate the square root of the right side: 2.937504003 Break this problem into two subproblems by setting (x + -3.876863133) equal to 2.937504003 and -2.937504003.Subproblem 1
x + -3.876863133 = 2.937504003 Simplifying x + -3.876863133 = 2.937504003 Reorder the terms: -3.876863133 + x = 2.937504003 Solving -3.876863133 + x = 2.937504003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.876863133' to each side of the equation. -3.876863133 + 3.876863133 + x = 2.937504003 + 3.876863133 Combine like terms: -3.876863133 + 3.876863133 = 0.000000000 0.000000000 + x = 2.937504003 + 3.876863133 x = 2.937504003 + 3.876863133 Combine like terms: 2.937504003 + 3.876863133 = 6.814367136 x = 6.814367136 Simplifying x = 6.814367136Subproblem 2
x + -3.876863133 = -2.937504003 Simplifying x + -3.876863133 = -2.937504003 Reorder the terms: -3.876863133 + x = -2.937504003 Solving -3.876863133 + x = -2.937504003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.876863133' to each side of the equation. -3.876863133 + 3.876863133 + x = -2.937504003 + 3.876863133 Combine like terms: -3.876863133 + 3.876863133 = 0.000000000 0.000000000 + x = -2.937504003 + 3.876863133 x = -2.937504003 + 3.876863133 Combine like terms: -2.937504003 + 3.876863133 = 0.93935913 x = 0.93935913 Simplifying x = 0.93935913Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.814367136, 0.93935913}
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