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Simplifying 4.9x2 + -7x + -105 = 0 Reorder the terms: -105 + -7x + 4.9x2 = 0 Solving -105 + -7x + 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'. -21.42857143 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '21.42857143' to each side of the equation. -21.42857143 + -1.428571429x + 21.42857143 + x2 = 0 + 21.42857143 Reorder the terms: -21.42857143 + 21.42857143 + -1.428571429x + x2 = 0 + 21.42857143 Combine like terms: -21.42857143 + 21.42857143 = 0.00000000 0.00000000 + -1.428571429x + x2 = 0 + 21.42857143 -1.428571429x + x2 = 0 + 21.42857143 Combine like terms: 0 + 21.42857143 = 21.42857143 -1.428571429x + x2 = 21.42857143 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 21.42857143 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 21.42857143 + 0.5102040819 Combine like terms: 21.42857143 + 0.5102040819 = 21.9387755119 0.5102040819 + -1.428571429x + x2 = 21.9387755119 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 21.9387755119 Calculate the square root of the right side: 4.68388466 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 4.68388466 and -4.68388466.Subproblem 1
x + -0.7142857145 = 4.68388466 Simplifying x + -0.7142857145 = 4.68388466 Reorder the terms: -0.7142857145 + x = 4.68388466 Solving -0.7142857145 + x = 4.68388466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 4.68388466 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 4.68388466 + 0.7142857145 x = 4.68388466 + 0.7142857145 Combine like terms: 4.68388466 + 0.7142857145 = 5.3981703745 x = 5.3981703745 Simplifying x = 5.3981703745Subproblem 2
x + -0.7142857145 = -4.68388466 Simplifying x + -0.7142857145 = -4.68388466 Reorder the terms: -0.7142857145 + x = -4.68388466 Solving -0.7142857145 + x = -4.68388466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -4.68388466 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -4.68388466 + 0.7142857145 x = -4.68388466 + 0.7142857145 Combine like terms: -4.68388466 + 0.7142857145 = -3.9695989455 x = -3.9695989455 Simplifying x = -3.9695989455Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3981703745, -3.9695989455}
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