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Simplifying 989 + -264x + 12x2 = 0 Solving 989 + -264x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 82.41666667 + -22x + x2 = 0 Move the constant term to the right: Add '-82.41666667' to each side of the equation. 82.41666667 + -22x + -82.41666667 + x2 = 0 + -82.41666667 Reorder the terms: 82.41666667 + -82.41666667 + -22x + x2 = 0 + -82.41666667 Combine like terms: 82.41666667 + -82.41666667 = 0.00000000 0.00000000 + -22x + x2 = 0 + -82.41666667 -22x + x2 = 0 + -82.41666667 Combine like terms: 0 + -82.41666667 = -82.41666667 -22x + x2 = -82.41666667 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -82.41666667 + 121 Reorder the terms: 121 + -22x + x2 = -82.41666667 + 121 Combine like terms: -82.41666667 + 121 = 38.58333333 121 + -22x + x2 = 38.58333333 Factor a perfect square on the left side: (x + -11)(x + -11) = 38.58333333 Calculate the square root of the right side: 6.211548384 Break this problem into two subproblems by setting (x + -11) equal to 6.211548384 and -6.211548384.Subproblem 1
x + -11 = 6.211548384 Simplifying x + -11 = 6.211548384 Reorder the terms: -11 + x = 6.211548384 Solving -11 + x = 6.211548384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 6.211548384 + 11 Combine like terms: -11 + 11 = 0 0 + x = 6.211548384 + 11 x = 6.211548384 + 11 Combine like terms: 6.211548384 + 11 = 17.211548384 x = 17.211548384 Simplifying x = 17.211548384Subproblem 2
x + -11 = -6.211548384 Simplifying x + -11 = -6.211548384 Reorder the terms: -11 + x = -6.211548384 Solving -11 + x = -6.211548384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -6.211548384 + 11 Combine like terms: -11 + 11 = 0 0 + x = -6.211548384 + 11 x = -6.211548384 + 11 Combine like terms: -6.211548384 + 11 = 4.788451616 x = 4.788451616 Simplifying x = 4.788451616Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.211548384, 4.788451616}
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