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Simplifying x = 12x2 + -112x + 196 Reorder the terms: x = 196 + -112x + 12x2 Solving x = 196 + -112x + 12x2 Solving for variable 'x'. Reorder the terms: -196 + x + 112x + -12x2 = 196 + -112x + 12x2 + -196 + 112x + -12x2 Combine like terms: x + 112x = 113x -196 + 113x + -12x2 = 196 + -112x + 12x2 + -196 + 112x + -12x2 Reorder the terms: -196 + 113x + -12x2 = 196 + -196 + -112x + 112x + 12x2 + -12x2 Combine like terms: 196 + -196 = 0 -196 + 113x + -12x2 = 0 + -112x + 112x + 12x2 + -12x2 -196 + 113x + -12x2 = -112x + 112x + 12x2 + -12x2 Combine like terms: -112x + 112x = 0 -196 + 113x + -12x2 = 0 + 12x2 + -12x2 -196 + 113x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -196 + 113x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 16.33333333 + -9.416666667x + x2 = 0 Move the constant term to the right: Add '-16.33333333' to each side of the equation. 16.33333333 + -9.416666667x + -16.33333333 + x2 = 0 + -16.33333333 Reorder the terms: 16.33333333 + -16.33333333 + -9.416666667x + x2 = 0 + -16.33333333 Combine like terms: 16.33333333 + -16.33333333 = 0.00000000 0.00000000 + -9.416666667x + x2 = 0 + -16.33333333 -9.416666667x + x2 = 0 + -16.33333333 Combine like terms: 0 + -16.33333333 = -16.33333333 -9.416666667x + x2 = -16.33333333 The x term is -9.416666667x. Take half its coefficient (-4.708333334). Square it (22.16840278) and add it to both sides. Add '22.16840278' to each side of the equation. -9.416666667x + 22.16840278 + x2 = -16.33333333 + 22.16840278 Reorder the terms: 22.16840278 + -9.416666667x + x2 = -16.33333333 + 22.16840278 Combine like terms: -16.33333333 + 22.16840278 = 5.83506945 22.16840278 + -9.416666667x + x2 = 5.83506945 Factor a perfect square on the left side: (x + -4.708333334)(x + -4.708333334) = 5.83506945 Calculate the square root of the right side: 2.415588841 Break this problem into two subproblems by setting (x + -4.708333334) equal to 2.415588841 and -2.415588841.Subproblem 1
x + -4.708333334 = 2.415588841 Simplifying x + -4.708333334 = 2.415588841 Reorder the terms: -4.708333334 + x = 2.415588841 Solving -4.708333334 + x = 2.415588841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.708333334' to each side of the equation. -4.708333334 + 4.708333334 + x = 2.415588841 + 4.708333334 Combine like terms: -4.708333334 + 4.708333334 = 0.000000000 0.000000000 + x = 2.415588841 + 4.708333334 x = 2.415588841 + 4.708333334 Combine like terms: 2.415588841 + 4.708333334 = 7.123922175 x = 7.123922175 Simplifying x = 7.123922175Subproblem 2
x + -4.708333334 = -2.415588841 Simplifying x + -4.708333334 = -2.415588841 Reorder the terms: -4.708333334 + x = -2.415588841 Solving -4.708333334 + x = -2.415588841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.708333334' to each side of the equation. -4.708333334 + 4.708333334 + x = -2.415588841 + 4.708333334 Combine like terms: -4.708333334 + 4.708333334 = 0.000000000 0.000000000 + x = -2.415588841 + 4.708333334 x = -2.415588841 + 4.708333334 Combine like terms: -2.415588841 + 4.708333334 = 2.292744493 x = 2.292744493 Simplifying x = 2.292744493Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.123922175, 2.292744493}
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