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Simplifying (x + 2)(x + 2) = -16x Reorder the terms: (2 + x)(x + 2) = -16x Reorder the terms: (2 + x)(2 + x) = -16x Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x)) = -16x ((2 * 2 + x * 2) + x(2 + x)) = -16x ((4 + 2x) + x(2 + x)) = -16x (4 + 2x + (2 * x + x * x)) = -16x (4 + 2x + (2x + x2)) = -16x Combine like terms: 2x + 2x = 4x (4 + 4x + x2) = -16x Solving 4 + 4x + x2 = -16x Solving for variable 'x'. Reorder the terms: 4 + 4x + 16x + x2 = -16x + 16x Combine like terms: 4x + 16x = 20x 4 + 20x + x2 = -16x + 16x Combine like terms: -16x + 16x = 0 4 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 20x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 20x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 20x + x2 = 0 + -4 20x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 20x + x2 = -4 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -4 + 100 Reorder the terms: 100 + 20x + x2 = -4 + 100 Combine like terms: -4 + 100 = 96 100 + 20x + x2 = 96 Factor a perfect square on the left side: (x + 10)(x + 10) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 10) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 10 = 9.797958971 Simplifying x + 10 = 9.797958971 Reorder the terms: 10 + x = 9.797958971 Solving 10 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.797958971 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.797958971 + -10 x = 9.797958971 + -10 Combine like terms: 9.797958971 + -10 = -0.202041029 x = -0.202041029 Simplifying x = -0.202041029Subproblem 2
x + 10 = -9.797958971 Simplifying x + 10 = -9.797958971 Reorder the terms: 10 + x = -9.797958971 Solving 10 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.797958971 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.797958971 + -10 x = -9.797958971 + -10 Combine like terms: -9.797958971 + -10 = -19.797958971 x = -19.797958971 Simplifying x = -19.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.202041029, -19.797958971}
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