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Simplifying 116.2396354x2 + 3332.382299x + 23564.48 = 0 Reorder the terms: 23564.48 + 3332.382299x + 116.2396354x2 = 0 Solving 23564.48 + 3332.382299x + 116.2396354x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 116.2396354 the coefficient of the squared term: Divide each side by '116.2396354'. 202.7232787 + 28.66821018x + x2 = 0 Move the constant term to the right: Add '-202.7232787' to each side of the equation. 202.7232787 + 28.66821018x + -202.7232787 + x2 = 0 + -202.7232787 Reorder the terms: 202.7232787 + -202.7232787 + 28.66821018x + x2 = 0 + -202.7232787 Combine like terms: 202.7232787 + -202.7232787 = 0.0000000 0.0000000 + 28.66821018x + x2 = 0 + -202.7232787 28.66821018x + x2 = 0 + -202.7232787 Combine like terms: 0 + -202.7232787 = -202.7232787 28.66821018x + x2 = -202.7232787 The x term is 28.66821018x. Take half its coefficient (14.33410509). Square it (205.4665687) and add it to both sides. Add '205.4665687' to each side of the equation. 28.66821018x + 205.4665687 + x2 = -202.7232787 + 205.4665687 Reorder the terms: 205.4665687 + 28.66821018x + x2 = -202.7232787 + 205.4665687 Combine like terms: -202.7232787 + 205.4665687 = 2.74329 205.4665687 + 28.66821018x + x2 = 2.74329 Factor a perfect square on the left side: (x + 14.33410509)(x + 14.33410509) = 2.74329 Calculate the square root of the right side: 1.656288018 Break this problem into two subproblems by setting (x + 14.33410509) equal to 1.656288018 and -1.656288018.Subproblem 1
x + 14.33410509 = 1.656288018 Simplifying x + 14.33410509 = 1.656288018 Reorder the terms: 14.33410509 + x = 1.656288018 Solving 14.33410509 + x = 1.656288018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.33410509' to each side of the equation. 14.33410509 + -14.33410509 + x = 1.656288018 + -14.33410509 Combine like terms: 14.33410509 + -14.33410509 = 0.00000000 0.00000000 + x = 1.656288018 + -14.33410509 x = 1.656288018 + -14.33410509 Combine like terms: 1.656288018 + -14.33410509 = -12.677817072 x = -12.677817072 Simplifying x = -12.677817072Subproblem 2
x + 14.33410509 = -1.656288018 Simplifying x + 14.33410509 = -1.656288018 Reorder the terms: 14.33410509 + x = -1.656288018 Solving 14.33410509 + x = -1.656288018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.33410509' to each side of the equation. 14.33410509 + -14.33410509 + x = -1.656288018 + -14.33410509 Combine like terms: 14.33410509 + -14.33410509 = 0.00000000 0.00000000 + x = -1.656288018 + -14.33410509 x = -1.656288018 + -14.33410509 Combine like terms: -1.656288018 + -14.33410509 = -15.990393108 x = -15.990393108 Simplifying x = -15.990393108Solution
The solution to the problem is based on the solutions from the subproblems. x = {-12.677817072, -15.990393108}
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