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Simplifying 0 = -4.9x2 + -8x + 8.26 Reorder the terms: 0 = 8.26 + -8x + -4.9x2 Solving 0 = 8.26 + -8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -8.26 = -8.26 -8.26 + 8x + 4.9x2 = 8.26 + -8x + -4.9x2 + -8.26 + 8x + 4.9x2 Reorder the terms: -8.26 + 8x + 4.9x2 = 8.26 + -8.26 + -8x + 8x + -4.9x2 + 4.9x2 Combine like terms: 8.26 + -8.26 = 0.00 -8.26 + 8x + 4.9x2 = 0.00 + -8x + 8x + -4.9x2 + 4.9x2 -8.26 + 8x + 4.9x2 = -8x + 8x + -4.9x2 + 4.9x2 Combine like terms: -8x + 8x = 0 -8.26 + 8x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -8.26 + 8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -8.26 + 8x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.685714286 + 1.632653061x + x2 = 0 Move the constant term to the right: Add '1.685714286' to each side of the equation. -1.685714286 + 1.632653061x + 1.685714286 + x2 = 0 + 1.685714286 Reorder the terms: -1.685714286 + 1.685714286 + 1.632653061x + x2 = 0 + 1.685714286 Combine like terms: -1.685714286 + 1.685714286 = 0.000000000 0.000000000 + 1.632653061x + x2 = 0 + 1.685714286 1.632653061x + x2 = 0 + 1.685714286 Combine like terms: 0 + 1.685714286 = 1.685714286 1.632653061x + x2 = 1.685714286 The x term is 1.632653061x. Take half its coefficient (0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. 1.632653061x + 0.6663890044 + x2 = 1.685714286 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061x + x2 = 1.685714286 + 0.6663890044 Combine like terms: 1.685714286 + 0.6663890044 = 2.3521032904 0.6663890044 + 1.632653061x + x2 = 2.3521032904 Factor a perfect square on the left side: (x + 0.8163265305)(x + 0.8163265305) = 2.3521032904 Calculate the square root of the right side: 1.533656836 Break this problem into two subproblems by setting (x + 0.8163265305) equal to 1.533656836 and -1.533656836.Subproblem 1
x + 0.8163265305 = 1.533656836 Simplifying x + 0.8163265305 = 1.533656836 Reorder the terms: 0.8163265305 + x = 1.533656836 Solving 0.8163265305 + x = 1.533656836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + x = 1.533656836 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + x = 1.533656836 + -0.8163265305 x = 1.533656836 + -0.8163265305 Combine like terms: 1.533656836 + -0.8163265305 = 0.7173303055 x = 0.7173303055 Simplifying x = 0.7173303055Subproblem 2
x + 0.8163265305 = -1.533656836 Simplifying x + 0.8163265305 = -1.533656836 Reorder the terms: 0.8163265305 + x = -1.533656836 Solving 0.8163265305 + x = -1.533656836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + x = -1.533656836 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + x = -1.533656836 + -0.8163265305 x = -1.533656836 + -0.8163265305 Combine like terms: -1.533656836 + -0.8163265305 = -2.3499833665 x = -2.3499833665 Simplifying x = -2.3499833665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7173303055, -2.3499833665}
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