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Simplifying 27.916x2 + 1046.867x + -14686 = 0 Reorder the terms: -14686 + 1046.867x + 27.916x2 = 0 Solving -14686 + 1046.867x + 27.916x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27.916 the coefficient of the squared term: Divide each side by '27.916'. -526.0782347 + 37.50060897x + x2 = 0 Move the constant term to the right: Add '526.0782347' to each side of the equation. -526.0782347 + 37.50060897x + 526.0782347 + x2 = 0 + 526.0782347 Reorder the terms: -526.0782347 + 526.0782347 + 37.50060897x + x2 = 0 + 526.0782347 Combine like terms: -526.0782347 + 526.0782347 = 0.0000000 0.0000000 + 37.50060897x + x2 = 0 + 526.0782347 37.50060897x + x2 = 0 + 526.0782347 Combine like terms: 0 + 526.0782347 = 526.0782347 37.50060897x + x2 = 526.0782347 The x term is 37.50060897x. Take half its coefficient (18.75030449). Square it (351.5739185) and add it to both sides. Add '351.5739185' to each side of the equation. 37.50060897x + 351.5739185 + x2 = 526.0782347 + 351.5739185 Reorder the terms: 351.5739185 + 37.50060897x + x2 = 526.0782347 + 351.5739185 Combine like terms: 526.0782347 + 351.5739185 = 877.6521532 351.5739185 + 37.50060897x + x2 = 877.6521532 Factor a perfect square on the left side: (x + 18.75030449)(x + 18.75030449) = 877.6521532 Calculate the square root of the right side: 29.625194568 Break this problem into two subproblems by setting (x + 18.75030449) equal to 29.625194568 and -29.625194568.Subproblem 1
x + 18.75030449 = 29.625194568 Simplifying x + 18.75030449 = 29.625194568 Reorder the terms: 18.75030449 + x = 29.625194568 Solving 18.75030449 + x = 29.625194568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75030449' to each side of the equation. 18.75030449 + -18.75030449 + x = 29.625194568 + -18.75030449 Combine like terms: 18.75030449 + -18.75030449 = 0.00000000 0.00000000 + x = 29.625194568 + -18.75030449 x = 29.625194568 + -18.75030449 Combine like terms: 29.625194568 + -18.75030449 = 10.874890078 x = 10.874890078 Simplifying x = 10.874890078Subproblem 2
x + 18.75030449 = -29.625194568 Simplifying x + 18.75030449 = -29.625194568 Reorder the terms: 18.75030449 + x = -29.625194568 Solving 18.75030449 + x = -29.625194568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75030449' to each side of the equation. 18.75030449 + -18.75030449 + x = -29.625194568 + -18.75030449 Combine like terms: 18.75030449 + -18.75030449 = 0.00000000 0.00000000 + x = -29.625194568 + -18.75030449 x = -29.625194568 + -18.75030449 Combine like terms: -29.625194568 + -18.75030449 = -48.375499058 x = -48.375499058 Simplifying x = -48.375499058Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.874890078, -48.375499058}
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