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Simplifying 4.9x2 + 336x + -806.4 = 0 Reorder the terms: -806.4 + 336x + 4.9x2 = 0 Solving -806.4 + 336x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -164.5714286 + 68.57142857x + x2 = 0 Move the constant term to the right: Add '164.5714286' to each side of the equation. -164.5714286 + 68.57142857x + 164.5714286 + x2 = 0 + 164.5714286 Reorder the terms: -164.5714286 + 164.5714286 + 68.57142857x + x2 = 0 + 164.5714286 Combine like terms: -164.5714286 + 164.5714286 = 0.0000000 0.0000000 + 68.57142857x + x2 = 0 + 164.5714286 68.57142857x + x2 = 0 + 164.5714286 Combine like terms: 0 + 164.5714286 = 164.5714286 68.57142857x + x2 = 164.5714286 The x term is 68.57142857x. Take half its coefficient (34.28571429). Square it (1175.510204) and add it to both sides. Add '1175.510204' to each side of the equation. 68.57142857x + 1175.510204 + x2 = 164.5714286 + 1175.510204 Reorder the terms: 1175.510204 + 68.57142857x + x2 = 164.5714286 + 1175.510204 Combine like terms: 164.5714286 + 1175.510204 = 1340.0816326 1175.510204 + 68.57142857x + x2 = 1340.0816326 Factor a perfect square on the left side: (x + 34.28571429)(x + 34.28571429) = 1340.0816326 Calculate the square root of the right side: 36.607125435 Break this problem into two subproblems by setting (x + 34.28571429) equal to 36.607125435 and -36.607125435.Subproblem 1
x + 34.28571429 = 36.607125435 Simplifying x + 34.28571429 = 36.607125435 Reorder the terms: 34.28571429 + x = 36.607125435 Solving 34.28571429 + x = 36.607125435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.28571429' to each side of the equation. 34.28571429 + -34.28571429 + x = 36.607125435 + -34.28571429 Combine like terms: 34.28571429 + -34.28571429 = 0.00000000 0.00000000 + x = 36.607125435 + -34.28571429 x = 36.607125435 + -34.28571429 Combine like terms: 36.607125435 + -34.28571429 = 2.321411145 x = 2.321411145 Simplifying x = 2.321411145Subproblem 2
x + 34.28571429 = -36.607125435 Simplifying x + 34.28571429 = -36.607125435 Reorder the terms: 34.28571429 + x = -36.607125435 Solving 34.28571429 + x = -36.607125435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.28571429' to each side of the equation. 34.28571429 + -34.28571429 + x = -36.607125435 + -34.28571429 Combine like terms: 34.28571429 + -34.28571429 = 0.00000000 0.00000000 + x = -36.607125435 + -34.28571429 x = -36.607125435 + -34.28571429 Combine like terms: -36.607125435 + -34.28571429 = -70.892839725 x = -70.892839725 Simplifying x = -70.892839725Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.321411145, -70.892839725}
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