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Simplifying x2 + 32x + -146 = 0 Reorder the terms: -146 + 32x + x2 = 0 Solving -146 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + 32x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + 32x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + 32x + x2 = 0 + 146 32x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 32x + x2 = 146 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 146 + 256 Reorder the terms: 256 + 32x + x2 = 146 + 256 Combine like terms: 146 + 256 = 402 256 + 32x + x2 = 402 Factor a perfect square on the left side: (x + 16)(x + 16) = 402 Calculate the square root of the right side: 20.049937656 Break this problem into two subproblems by setting (x + 16) equal to 20.049937656 and -20.049937656.Subproblem 1
x + 16 = 20.049937656 Simplifying x + 16 = 20.049937656 Reorder the terms: 16 + x = 20.049937656 Solving 16 + x = 20.049937656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 20.049937656 + -16 Combine like terms: 16 + -16 = 0 0 + x = 20.049937656 + -16 x = 20.049937656 + -16 Combine like terms: 20.049937656 + -16 = 4.049937656 x = 4.049937656 Simplifying x = 4.049937656Subproblem 2
x + 16 = -20.049937656 Simplifying x + 16 = -20.049937656 Reorder the terms: 16 + x = -20.049937656 Solving 16 + x = -20.049937656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -20.049937656 + -16 Combine like terms: 16 + -16 = 0 0 + x = -20.049937656 + -16 x = -20.049937656 + -16 Combine like terms: -20.049937656 + -16 = -36.049937656 x = -36.049937656 Simplifying x = -36.049937656Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.049937656, -36.049937656}
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