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Simplifying -0.059x2 + 2.6x + 19 = 0 Reorder the terms: 19 + 2.6x + -0.059x2 = 0 Solving 19 + 2.6x + -0.059x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.059 the coefficient of the squared term: Divide each side by '-0.059'. -322.0338983 + -44.06779661x + x2 = 0 Move the constant term to the right: Add '322.0338983' to each side of the equation. -322.0338983 + -44.06779661x + 322.0338983 + x2 = 0 + 322.0338983 Reorder the terms: -322.0338983 + 322.0338983 + -44.06779661x + x2 = 0 + 322.0338983 Combine like terms: -322.0338983 + 322.0338983 = 0.0000000 0.0000000 + -44.06779661x + x2 = 0 + 322.0338983 -44.06779661x + x2 = 0 + 322.0338983 Combine like terms: 0 + 322.0338983 = 322.0338983 -44.06779661x + x2 = 322.0338983 The x term is -44.06779661x. Take half its coefficient (-22.03389831). Square it (485.4926747) and add it to both sides. Add '485.4926747' to each side of the equation. -44.06779661x + 485.4926747 + x2 = 322.0338983 + 485.4926747 Reorder the terms: 485.4926747 + -44.06779661x + x2 = 322.0338983 + 485.4926747 Combine like terms: 322.0338983 + 485.4926747 = 807.526573 485.4926747 + -44.06779661x + x2 = 807.526573 Factor a perfect square on the left side: (x + -22.03389831)(x + -22.03389831) = 807.526573 Calculate the square root of the right side: 28.417012035 Break this problem into two subproblems by setting (x + -22.03389831) equal to 28.417012035 and -28.417012035.Subproblem 1
x + -22.03389831 = 28.417012035 Simplifying x + -22.03389831 = 28.417012035 Reorder the terms: -22.03389831 + x = 28.417012035 Solving -22.03389831 + x = 28.417012035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.03389831' to each side of the equation. -22.03389831 + 22.03389831 + x = 28.417012035 + 22.03389831 Combine like terms: -22.03389831 + 22.03389831 = 0.00000000 0.00000000 + x = 28.417012035 + 22.03389831 x = 28.417012035 + 22.03389831 Combine like terms: 28.417012035 + 22.03389831 = 50.450910345 x = 50.450910345 Simplifying x = 50.450910345Subproblem 2
x + -22.03389831 = -28.417012035 Simplifying x + -22.03389831 = -28.417012035 Reorder the terms: -22.03389831 + x = -28.417012035 Solving -22.03389831 + x = -28.417012035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.03389831' to each side of the equation. -22.03389831 + 22.03389831 + x = -28.417012035 + 22.03389831 Combine like terms: -22.03389831 + 22.03389831 = 0.00000000 0.00000000 + x = -28.417012035 + 22.03389831 x = -28.417012035 + 22.03389831 Combine like terms: -28.417012035 + 22.03389831 = -6.383113725 x = -6.383113725 Simplifying x = -6.383113725Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.450910345, -6.383113725}
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