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Simplifying 5619.7x2 + 137715.5x + -60452000 = 0 Reorder the terms: -60452000 + 137715.5x + 5619.7x2 = 0 Solving -60452000 + 137715.5x + 5619.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5619.7 the coefficient of the squared term: Divide each side by '5619.7'. -10757.15786 + 24.50584551x + x2 = 0 Move the constant term to the right: Add '10757.15786' to each side of the equation. -10757.15786 + 24.50584551x + 10757.15786 + x2 = 0 + 10757.15786 Reorder the terms: -10757.15786 + 10757.15786 + 24.50584551x + x2 = 0 + 10757.15786 Combine like terms: -10757.15786 + 10757.15786 = 0.00000 0.00000 + 24.50584551x + x2 = 0 + 10757.15786 24.50584551x + x2 = 0 + 10757.15786 Combine like terms: 0 + 10757.15786 = 10757.15786 24.50584551x + x2 = 10757.15786 The x term is 24.50584551x. Take half its coefficient (12.25292276). Square it (150.1341162) and add it to both sides. Add '150.1341162' to each side of the equation. 24.50584551x + 150.1341162 + x2 = 10757.15786 + 150.1341162 Reorder the terms: 150.1341162 + 24.50584551x + x2 = 10757.15786 + 150.1341162 Combine like terms: 10757.15786 + 150.1341162 = 10907.2919762 150.1341162 + 24.50584551x + x2 = 10907.2919762 Factor a perfect square on the left side: (x + 12.25292276)(x + 12.25292276) = 10907.2919762 Calculate the square root of the right side: 104.437981483 Break this problem into two subproblems by setting (x + 12.25292276) equal to 104.437981483 and -104.437981483.Subproblem 1
x + 12.25292276 = 104.437981483 Simplifying x + 12.25292276 = 104.437981483 Reorder the terms: 12.25292276 + x = 104.437981483 Solving 12.25292276 + x = 104.437981483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25292276' to each side of the equation. 12.25292276 + -12.25292276 + x = 104.437981483 + -12.25292276 Combine like terms: 12.25292276 + -12.25292276 = 0.00000000 0.00000000 + x = 104.437981483 + -12.25292276 x = 104.437981483 + -12.25292276 Combine like terms: 104.437981483 + -12.25292276 = 92.185058723 x = 92.185058723 Simplifying x = 92.185058723Subproblem 2
x + 12.25292276 = -104.437981483 Simplifying x + 12.25292276 = -104.437981483 Reorder the terms: 12.25292276 + x = -104.437981483 Solving 12.25292276 + x = -104.437981483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25292276' to each side of the equation. 12.25292276 + -12.25292276 + x = -104.437981483 + -12.25292276 Combine like terms: 12.25292276 + -12.25292276 = 0.00000000 0.00000000 + x = -104.437981483 + -12.25292276 x = -104.437981483 + -12.25292276 Combine like terms: -104.437981483 + -12.25292276 = -116.690904243 x = -116.690904243 Simplifying x = -116.690904243Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.185058723, -116.690904243}
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