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Simplifying x2 + 16x + -42 = -4 Reorder the terms: -42 + 16x + x2 = -4 Solving -42 + 16x + x2 = -4 Solving for variable 'x'. Reorder the terms: -42 + 4 + 16x + x2 = -4 + 4 Combine like terms: -42 + 4 = -38 -38 + 16x + x2 = -4 + 4 Combine like terms: -4 + 4 = 0 -38 + 16x + x2 = 0 Begin completing the square. 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 = 2.099504938 x = 2.099504938 Simplifying x = 2.099504938Subproblem 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 = -18.099504938 x = -18.099504938 Simplifying x = -18.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.099504938, -18.099504938}
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