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Simplifying 4.9x2 + -24x + 19 = 0 Reorder the terms: 19 + -24x + 4.9x2 = 0 Solving 19 + -24x + 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'. 3.87755102 + -4.897959184x + x2 = 0 Move the constant term to the right: Add '-3.87755102' to each side of the equation. 3.87755102 + -4.897959184x + -3.87755102 + x2 = 0 + -3.87755102 Reorder the terms: 3.87755102 + -3.87755102 + -4.897959184x + x2 = 0 + -3.87755102 Combine like terms: 3.87755102 + -3.87755102 = 0.00000000 0.00000000 + -4.897959184x + x2 = 0 + -3.87755102 -4.897959184x + x2 = 0 + -3.87755102 Combine like terms: 0 + -3.87755102 = -3.87755102 -4.897959184x + x2 = -3.87755102 The x term is -4.897959184x. Take half its coefficient (-2.448979592). Square it (5.997501042) and add it to both sides. Add '5.997501042' to each side of the equation. -4.897959184x + 5.997501042 + x2 = -3.87755102 + 5.997501042 Reorder the terms: 5.997501042 + -4.897959184x + x2 = -3.87755102 + 5.997501042 Combine like terms: -3.87755102 + 5.997501042 = 2.119950022 5.997501042 + -4.897959184x + x2 = 2.119950022 Factor a perfect square on the left side: (x + -2.448979592)(x + -2.448979592) = 2.119950022 Calculate the square root of the right side: 1.456004815 Break this problem into two subproblems by setting (x + -2.448979592) equal to 1.456004815 and -1.456004815.Subproblem 1
x + -2.448979592 = 1.456004815 Simplifying x + -2.448979592 = 1.456004815 Reorder the terms: -2.448979592 + x = 1.456004815 Solving -2.448979592 + x = 1.456004815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + x = 1.456004815 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + x = 1.456004815 + 2.448979592 x = 1.456004815 + 2.448979592 Combine like terms: 1.456004815 + 2.448979592 = 3.904984407 x = 3.904984407 Simplifying x = 3.904984407Subproblem 2
x + -2.448979592 = -1.456004815 Simplifying x + -2.448979592 = -1.456004815 Reorder the terms: -2.448979592 + x = -1.456004815 Solving -2.448979592 + x = -1.456004815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + x = -1.456004815 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + x = -1.456004815 + 2.448979592 x = -1.456004815 + 2.448979592 Combine like terms: -1.456004815 + 2.448979592 = 0.992974777 x = 0.992974777 Simplifying x = 0.992974777Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.904984407, 0.992974777}
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