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Simplifying x2 + 30 = -16x Reorder the terms: 30 + x2 = -16x Solving 30 + x2 = -16x Solving for variable 'x'. Reorder the terms: 30 + 16x + x2 = -16x + 16x Combine like terms: -16x + 16x = 0 30 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 16x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 16x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 16x + x2 = 0 + -30 16x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 16x + x2 = -30 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 = -30 + 64 Reorder the terms: 64 + 16x + x2 = -30 + 64 Combine like terms: -30 + 64 = 34 64 + 16x + x2 = 34 Factor a perfect square on the left side: (x + 8)(x + 8) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 8) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 8 = 5.830951895 Simplifying x + 8 = 5.830951895 Reorder the terms: 8 + x = 5.830951895 Solving 8 + x = 5.830951895 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 = 5.830951895 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.830951895 + -8 x = 5.830951895 + -8 Combine like terms: 5.830951895 + -8 = -2.169048105 x = -2.169048105 Simplifying x = -2.169048105Subproblem 2
x + 8 = -5.830951895 Simplifying x + 8 = -5.830951895 Reorder the terms: 8 + x = -5.830951895 Solving 8 + x = -5.830951895 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 = -5.830951895 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.830951895 + -8 x = -5.830951895 + -8 Combine like terms: -5.830951895 + -8 = -13.830951895 x = -13.830951895 Simplifying x = -13.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.169048105, -13.830951895}
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