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Simplifying 6x = x2 + -12x + 2 Reorder the terms: 6x = 2 + -12x + x2 Solving 6x = 2 + -12x + x2 Solving for variable 'x'. Reorder the terms: -2 + 6x + 12x + -1x2 = 2 + -12x + x2 + -2 + 12x + -1x2 Combine like terms: 6x + 12x = 18x -2 + 18x + -1x2 = 2 + -12x + x2 + -2 + 12x + -1x2 Reorder the terms: -2 + 18x + -1x2 = 2 + -2 + -12x + 12x + x2 + -1x2 Combine like terms: 2 + -2 = 0 -2 + 18x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -2 + 18x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -2 + 18x + -1x2 = 0 + x2 + -1x2 -2 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -18x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -18x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -18x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -18x + x2 = 0 + -2 -18x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -18x + x2 = -2 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -2 + 81 Reorder the terms: 81 + -18x + x2 = -2 + 81 Combine like terms: -2 + 81 = 79 81 + -18x + x2 = 79 Factor a perfect square on the left side: (x + -9)(x + -9) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -9) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -9 = 8.888194417 Simplifying x + -9 = 8.888194417 Reorder the terms: -9 + x = 8.888194417 Solving -9 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.888194417 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.888194417 + 9 x = 8.888194417 + 9 Combine like terms: 8.888194417 + 9 = 17.888194417 x = 17.888194417 Simplifying x = 17.888194417Subproblem 2
x + -9 = -8.888194417 Simplifying x + -9 = -8.888194417 Reorder the terms: -9 + x = -8.888194417 Solving -9 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.888194417 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.888194417 + 9 x = -8.888194417 + 9 Combine like terms: -8.888194417 + 9 = 0.111805583 x = 0.111805583 Simplifying x = 0.111805583Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.888194417, 0.111805583}
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