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Simplifying 2750x2 + 5623x + -94972 = 0 Reorder the terms: -94972 + 5623x + 2750x2 = 0 Solving -94972 + 5623x + 2750x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2750 the coefficient of the squared term: Divide each side by '2750'. -34.53527273 + 2.044727273x + x2 = 0 Move the constant term to the right: Add '34.53527273' to each side of the equation. -34.53527273 + 2.044727273x + 34.53527273 + x2 = 0 + 34.53527273 Reorder the terms: -34.53527273 + 34.53527273 + 2.044727273x + x2 = 0 + 34.53527273 Combine like terms: -34.53527273 + 34.53527273 = 0.00000000 0.00000000 + 2.044727273x + x2 = 0 + 34.53527273 2.044727273x + x2 = 0 + 34.53527273 Combine like terms: 0 + 34.53527273 = 34.53527273 2.044727273x + x2 = 34.53527273 The x term is 2.044727273x. Take half its coefficient (1.022363637). Square it (1.045227406) and add it to both sides. Add '1.045227406' to each side of the equation. 2.044727273x + 1.045227406 + x2 = 34.53527273 + 1.045227406 Reorder the terms: 1.045227406 + 2.044727273x + x2 = 34.53527273 + 1.045227406 Combine like terms: 34.53527273 + 1.045227406 = 35.580500136 1.045227406 + 2.044727273x + x2 = 35.580500136 Factor a perfect square on the left side: (x + 1.022363637)(x + 1.022363637) = 35.580500136 Calculate the square root of the right side: 5.96493924 Break this problem into two subproblems by setting (x + 1.022363637) equal to 5.96493924 and -5.96493924.Subproblem 1
x + 1.022363637 = 5.96493924 Simplifying x + 1.022363637 = 5.96493924 Reorder the terms: 1.022363637 + x = 5.96493924 Solving 1.022363637 + x = 5.96493924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.022363637' to each side of the equation. 1.022363637 + -1.022363637 + x = 5.96493924 + -1.022363637 Combine like terms: 1.022363637 + -1.022363637 = 0.000000000 0.000000000 + x = 5.96493924 + -1.022363637 x = 5.96493924 + -1.022363637 Combine like terms: 5.96493924 + -1.022363637 = 4.942575603 x = 4.942575603 Simplifying x = 4.942575603Subproblem 2
x + 1.022363637 = -5.96493924 Simplifying x + 1.022363637 = -5.96493924 Reorder the terms: 1.022363637 + x = -5.96493924 Solving 1.022363637 + x = -5.96493924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.022363637' to each side of the equation. 1.022363637 + -1.022363637 + x = -5.96493924 + -1.022363637 Combine like terms: 1.022363637 + -1.022363637 = 0.000000000 0.000000000 + x = -5.96493924 + -1.022363637 x = -5.96493924 + -1.022363637 Combine like terms: -5.96493924 + -1.022363637 = -6.987302877 x = -6.987302877 Simplifying x = -6.987302877Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.942575603, -6.987302877}
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