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Simplifying 3.5 + 46.9x + -9.8x2 = 0 Solving 3.5 + 46.9x + -9.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -0.3571428571 + -4.785714286x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -4.785714286x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -4.785714286x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -4.785714286x + x2 = 0 + 0.3571428571 -4.785714286x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -4.785714286x + x2 = 0.3571428571 The x term is -4.785714286x. Take half its coefficient (-2.392857143). Square it (5.725765307) and add it to both sides. Add '5.725765307' to each side of the equation. -4.785714286x + 5.725765307 + x2 = 0.3571428571 + 5.725765307 Reorder the terms: 5.725765307 + -4.785714286x + x2 = 0.3571428571 + 5.725765307 Combine like terms: 0.3571428571 + 5.725765307 = 6.0829081641 5.725765307 + -4.785714286x + x2 = 6.0829081641 Factor a perfect square on the left side: (x + -2.392857143)(x + -2.392857143) = 6.0829081641 Calculate the square root of the right side: 2.466355239 Break this problem into two subproblems by setting (x + -2.392857143) equal to 2.466355239 and -2.466355239.Subproblem 1
x + -2.392857143 = 2.466355239 Simplifying x + -2.392857143 = 2.466355239 Reorder the terms: -2.392857143 + x = 2.466355239 Solving -2.392857143 + x = 2.466355239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.392857143' to each side of the equation. -2.392857143 + 2.392857143 + x = 2.466355239 + 2.392857143 Combine like terms: -2.392857143 + 2.392857143 = 0.000000000 0.000000000 + x = 2.466355239 + 2.392857143 x = 2.466355239 + 2.392857143 Combine like terms: 2.466355239 + 2.392857143 = 4.859212382 x = 4.859212382 Simplifying x = 4.859212382Subproblem 2
x + -2.392857143 = -2.466355239 Simplifying x + -2.392857143 = -2.466355239 Reorder the terms: -2.392857143 + x = -2.466355239 Solving -2.392857143 + x = -2.466355239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.392857143' to each side of the equation. -2.392857143 + 2.392857143 + x = -2.466355239 + 2.392857143 Combine like terms: -2.392857143 + 2.392857143 = 0.000000000 0.000000000 + x = -2.466355239 + 2.392857143 x = -2.466355239 + 2.392857143 Combine like terms: -2.466355239 + 2.392857143 = -0.073498096 x = -0.073498096 Simplifying x = -0.073498096Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.859212382, -0.073498096}
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