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Simplifying 0 = x2 + -16x + -38 Reorder the terms: 0 = -38 + -16x + x2 Solving 0 = -38 + -16x + x2 Solving for variable 'x'. Combine like terms: 0 + 38 = 38 38 + 16x + -1x2 = -38 + -16x + x2 + 38 + 16x + -1x2 Reorder the terms: 38 + 16x + -1x2 = -38 + 38 + -16x + 16x + x2 + -1x2 Combine like terms: -38 + 38 = 0 38 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2 38 + 16x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 38 + 16x + -1x2 = 0 + x2 + -1x2 38 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 38 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -38 + -16x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + -16x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -16x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -16x + x2 = 0 + 38 -16x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -16x + x2 = 38 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 38 + 64 Reorder the terms: 64 + -16x + x2 = 38 + 64 Combine like terms: 38 + 64 = 102 64 + -16x + x2 = 102 Factor a perfect square on the left side: (x + -8)(x + -8) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + -8) equal to 10.099504938 and -10.099504938.Subproblem 1
x + -8 = 10.099504938 Simplifying x + -8 = 10.099504938 Reorder the terms: -8 + x = 10.099504938 Solving -8 + x = 10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 10.099504938 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.099504938 + 8 x = 10.099504938 + 8 Combine like terms: 10.099504938 + 8 = 18.099504938 x = 18.099504938 Simplifying x = 18.099504938Subproblem 2
x + -8 = -10.099504938 Simplifying x + -8 = -10.099504938 Reorder the terms: -8 + x = -10.099504938 Solving -8 + x = -10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -10.099504938 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.099504938 + 8 x = -10.099504938 + 8 Combine like terms: -10.099504938 + 8 = -2.099504938 x = -2.099504938 Simplifying x = -2.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.099504938, -2.099504938}
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