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Simplifying x2 + 16x + -30 = 0 Reorder the terms: -30 + 16x + x2 = 0 Solving -30 + 16x + x2 = 0 Solving for variable 'x'. 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 = 94 64 + 16x + x2 = 94 Factor a perfect square on the left side: (x + 8)(x + 8) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 8) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 8 = 9.695359715 Simplifying x + 8 = 9.695359715 Reorder the terms: 8 + x = 9.695359715 Solving 8 + x = 9.695359715 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 = 9.695359715 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.695359715 + -8 x = 9.695359715 + -8 Combine like terms: 9.695359715 + -8 = 1.695359715 x = 1.695359715 Simplifying x = 1.695359715Subproblem 2
x + 8 = -9.695359715 Simplifying x + 8 = -9.695359715 Reorder the terms: 8 + x = -9.695359715 Solving 8 + x = -9.695359715 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 = -9.695359715 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.695359715 + -8 x = -9.695359715 + -8 Combine like terms: -9.695359715 + -8 = -17.695359715 x = -17.695359715 Simplifying x = -17.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.695359715, -17.695359715}
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