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Simplifying (x + -8) = 16 + -1x2 + 19x Reorder the terms: (-8 + x) = 16 + -1x2 + 19x Remove parenthesis around (-8 + x) -8 + x = 16 + -1x2 + 19x Reorder the terms: -8 + x = 16 + 19x + -1x2 Solving -8 + x = 16 + 19x + -1x2 Solving for variable 'x'. Reorder the terms: -8 + -16 + x + -19x + x2 = 16 + 19x + -1x2 + -16 + -19x + x2 Combine like terms: -8 + -16 = -24 -24 + x + -19x + x2 = 16 + 19x + -1x2 + -16 + -19x + x2 Combine like terms: x + -19x = -18x -24 + -18x + x2 = 16 + 19x + -1x2 + -16 + -19x + x2 Reorder the terms: -24 + -18x + x2 = 16 + -16 + 19x + -19x + -1x2 + x2 Combine like terms: 16 + -16 = 0 -24 + -18x + x2 = 0 + 19x + -19x + -1x2 + x2 -24 + -18x + x2 = 19x + -19x + -1x2 + x2 Combine like terms: 19x + -19x = 0 -24 + -18x + x2 = 0 + -1x2 + x2 -24 + -18x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -24 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -18x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -18x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -18x + x2 = 0 + 24 -18x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -18x + x2 = 24 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 = 24 + 81 Reorder the terms: 81 + -18x + x2 = 24 + 81 Combine like terms: 24 + 81 = 105 81 + -18x + x2 = 105 Factor a perfect square on the left side: (x + -9)(x + -9) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -9) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -9 = 10.246950766 Simplifying x + -9 = 10.246950766 Reorder the terms: -9 + x = 10.246950766 Solving -9 + x = 10.246950766 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 = 10.246950766 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.246950766 + 9 x = 10.246950766 + 9 Combine like terms: 10.246950766 + 9 = 19.246950766 x = 19.246950766 Simplifying x = 19.246950766Subproblem 2
x + -9 = -10.246950766 Simplifying x + -9 = -10.246950766 Reorder the terms: -9 + x = -10.246950766 Solving -9 + x = -10.246950766 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 = -10.246950766 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.246950766 + 9 x = -10.246950766 + 9 Combine like terms: -10.246950766 + 9 = -1.246950766 x = -1.246950766 Simplifying x = -1.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.246950766, -1.246950766}
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