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Simplifying 50 = 1.9x + 4.3x2 Solving 50 = 1.9x + 4.3x2 Solving for variable 'x'. Reorder the terms: 50 + -1.9x + -4.3x2 = 1.9x + -1.9x + 4.3x2 + -4.3x2 Combine like terms: 1.9x + -1.9x = 0.0 50 + -1.9x + -4.3x2 = 0.0 + 4.3x2 + -4.3x2 50 + -1.9x + -4.3x2 = 4.3x2 + -4.3x2 Combine like terms: 4.3x2 + -4.3x2 = 0.0 50 + -1.9x + -4.3x2 = 0.0 Begin completing the square. Divide all terms by -4.3 the coefficient of the squared term: Divide each side by '-4.3'. -11.62790698 + 0.4418604651x + x2 = 0 Move the constant term to the right: Add '11.62790698' to each side of the equation. -11.62790698 + 0.4418604651x + 11.62790698 + x2 = 0 + 11.62790698 Reorder the terms: -11.62790698 + 11.62790698 + 0.4418604651x + x2 = 0 + 11.62790698 Combine like terms: -11.62790698 + 11.62790698 = 0.00000000 0.00000000 + 0.4418604651x + x2 = 0 + 11.62790698 0.4418604651x + x2 = 0 + 11.62790698 Combine like terms: 0 + 11.62790698 = 11.62790698 0.4418604651x + x2 = 11.62790698 The x term is 0.4418604651x. Take half its coefficient (0.2209302326). Square it (0.04881016768) and add it to both sides. Add '0.04881016768' to each side of the equation. 0.4418604651x + 0.04881016768 + x2 = 11.62790698 + 0.04881016768 Reorder the terms: 0.04881016768 + 0.4418604651x + x2 = 11.62790698 + 0.04881016768 Combine like terms: 11.62790698 + 0.04881016768 = 11.67671714768 0.04881016768 + 0.4418604651x + x2 = 11.67671714768 Factor a perfect square on the left side: (x + 0.2209302326)(x + 0.2209302326) = 11.67671714768 Calculate the square root of the right side: 3.417121178 Break this problem into two subproblems by setting (x + 0.2209302326) equal to 3.417121178 and -3.417121178.Subproblem 1
x + 0.2209302326 = 3.417121178 Simplifying x + 0.2209302326 = 3.417121178 Reorder the terms: 0.2209302326 + x = 3.417121178 Solving 0.2209302326 + x = 3.417121178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2209302326' to each side of the equation. 0.2209302326 + -0.2209302326 + x = 3.417121178 + -0.2209302326 Combine like terms: 0.2209302326 + -0.2209302326 = 0.0000000000 0.0000000000 + x = 3.417121178 + -0.2209302326 x = 3.417121178 + -0.2209302326 Combine like terms: 3.417121178 + -0.2209302326 = 3.1961909454 x = 3.1961909454 Simplifying x = 3.1961909454Subproblem 2
x + 0.2209302326 = -3.417121178 Simplifying x + 0.2209302326 = -3.417121178 Reorder the terms: 0.2209302326 + x = -3.417121178 Solving 0.2209302326 + x = -3.417121178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2209302326' to each side of the equation. 0.2209302326 + -0.2209302326 + x = -3.417121178 + -0.2209302326 Combine like terms: 0.2209302326 + -0.2209302326 = 0.0000000000 0.0000000000 + x = -3.417121178 + -0.2209302326 x = -3.417121178 + -0.2209302326 Combine like terms: -3.417121178 + -0.2209302326 = -3.6380514106 x = -3.6380514106 Simplifying x = -3.6380514106Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1961909454, -3.6380514106}
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