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Simplifying 2x2 + -12x + 19 = x2 + 6x + -2 Reorder the terms: 19 + -12x + 2x2 = x2 + 6x + -2 Reorder the terms: 19 + -12x + 2x2 = -2 + 6x + x2 Solving 19 + -12x + 2x2 = -2 + 6x + x2 Solving for variable 'x'. Reorder the terms: 19 + 2 + -12x + -6x + 2x2 + -1x2 = -2 + 6x + x2 + 2 + -6x + -1x2 Combine like terms: 19 + 2 = 21 21 + -12x + -6x + 2x2 + -1x2 = -2 + 6x + x2 + 2 + -6x + -1x2 Combine like terms: -12x + -6x = -18x 21 + -18x + 2x2 + -1x2 = -2 + 6x + x2 + 2 + -6x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 21 + -18x + 1x2 = -2 + 6x + x2 + 2 + -6x + -1x2 Reorder the terms: 21 + -18x + 1x2 = -2 + 2 + 6x + -6x + x2 + -1x2 Combine like terms: -2 + 2 = 0 21 + -18x + 1x2 = 0 + 6x + -6x + x2 + -1x2 21 + -18x + 1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 21 + -18x + 1x2 = 0 + x2 + -1x2 21 + -18x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -18x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -18x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -18x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -18x + x2 = 0 + -21 -18x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -18x + x2 = -21 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 = -21 + 81 Reorder the terms: 81 + -18x + x2 = -21 + 81 Combine like terms: -21 + 81 = 60 81 + -18x + x2 = 60 Factor a perfect square on the left side: (x + -9)(x + -9) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -9) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -9 = 7.745966692 Simplifying x + -9 = 7.745966692 Reorder the terms: -9 + x = 7.745966692 Solving -9 + x = 7.745966692 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 = 7.745966692 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.745966692 + 9 x = 7.745966692 + 9 Combine like terms: 7.745966692 + 9 = 16.745966692 x = 16.745966692 Simplifying x = 16.745966692Subproblem 2
x + -9 = -7.745966692 Simplifying x + -9 = -7.745966692 Reorder the terms: -9 + x = -7.745966692 Solving -9 + x = -7.745966692 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 = -7.745966692 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.745966692 + 9 x = -7.745966692 + 9 Combine like terms: -7.745966692 + 9 = 1.254033308 x = 1.254033308 Simplifying x = 1.254033308Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.745966692, 1.254033308}
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