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Simplifying 2.515x2 = 21.044x + -3.837 Reorder the terms: 2.515x2 = -3.837 + 21.044x Solving 2.515x2 = -3.837 + 21.044x Solving for variable 'x'. Reorder the terms: 3.837 + -21.044x + 2.515x2 = -3.837 + 21.044x + 3.837 + -21.044x Reorder the terms: 3.837 + -21.044x + 2.515x2 = -3.837 + 3.837 + 21.044x + -21.044x Combine like terms: -3.837 + 3.837 = 0.000 3.837 + -21.044x + 2.515x2 = 0.000 + 21.044x + -21.044x 3.837 + -21.044x + 2.515x2 = 21.044x + -21.044x Combine like terms: 21.044x + -21.044x = 0.000 3.837 + -21.044x + 2.515x2 = 0.000 Begin completing the square. Divide all terms by 2.515 the coefficient of the squared term: Divide each side by '2.515'. 1.525646123 + -8.367395626x + x2 = 0 Move the constant term to the right: Add '-1.525646123' to each side of the equation. 1.525646123 + -8.367395626x + -1.525646123 + x2 = 0 + -1.525646123 Reorder the terms: 1.525646123 + -1.525646123 + -8.367395626x + x2 = 0 + -1.525646123 Combine like terms: 1.525646123 + -1.525646123 = 0.000000000 0.000000000 + -8.367395626x + x2 = 0 + -1.525646123 -8.367395626x + x2 = 0 + -1.525646123 Combine like terms: 0 + -1.525646123 = -1.525646123 -8.367395626x + x2 = -1.525646123 The x term is -8.367395626x. Take half its coefficient (-4.183697813). Square it (17.50332739) and add it to both sides. Add '17.50332739' to each side of the equation. -8.367395626x + 17.50332739 + x2 = -1.525646123 + 17.50332739 Reorder the terms: 17.50332739 + -8.367395626x + x2 = -1.525646123 + 17.50332739 Combine like terms: -1.525646123 + 17.50332739 = 15.977681267 17.50332739 + -8.367395626x + x2 = 15.977681267 Factor a perfect square on the left side: (x + -4.183697813)(x + -4.183697813) = 15.977681267 Calculate the square root of the right side: 3.997209185 Break this problem into two subproblems by setting (x + -4.183697813) equal to 3.997209185 and -3.997209185.Subproblem 1
x + -4.183697813 = 3.997209185 Simplifying x + -4.183697813 = 3.997209185 Reorder the terms: -4.183697813 + x = 3.997209185 Solving -4.183697813 + x = 3.997209185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.183697813' to each side of the equation. -4.183697813 + 4.183697813 + x = 3.997209185 + 4.183697813 Combine like terms: -4.183697813 + 4.183697813 = 0.000000000 0.000000000 + x = 3.997209185 + 4.183697813 x = 3.997209185 + 4.183697813 Combine like terms: 3.997209185 + 4.183697813 = 8.180906998 x = 8.180906998 Simplifying x = 8.180906998Subproblem 2
x + -4.183697813 = -3.997209185 Simplifying x + -4.183697813 = -3.997209185 Reorder the terms: -4.183697813 + x = -3.997209185 Solving -4.183697813 + x = -3.997209185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.183697813' to each side of the equation. -4.183697813 + 4.183697813 + x = -3.997209185 + 4.183697813 Combine like terms: -4.183697813 + 4.183697813 = 0.000000000 0.000000000 + x = -3.997209185 + 4.183697813 x = -3.997209185 + 4.183697813 Combine like terms: -3.997209185 + 4.183697813 = 0.186488628 x = 0.186488628 Simplifying x = 0.186488628Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.180906998, 0.186488628}
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