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Simplifying x2 + 32x + 4.8 = 0 Reorder the terms: 4.8 + 32x + x2 = 0 Solving 4.8 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + 32x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + 32x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + 32x + x2 = 0 + -4.8 32x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 32x + x2 = -4.8 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 = -4.8 + 256 Reorder the terms: 256 + 32x + x2 = -4.8 + 256 Combine like terms: -4.8 + 256 = 251.2 256 + 32x + x2 = 251.2 Factor a perfect square on the left side: (x + 16)(x + 16) = 251.2 Calculate the square root of the right side: 15.849290205 Break this problem into two subproblems by setting (x + 16) equal to 15.849290205 and -15.849290205.Subproblem 1
x + 16 = 15.849290205 Simplifying x + 16 = 15.849290205 Reorder the terms: 16 + x = 15.849290205 Solving 16 + x = 15.849290205 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 = 15.849290205 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.849290205 + -16 x = 15.849290205 + -16 Combine like terms: 15.849290205 + -16 = -0.150709795 x = -0.150709795 Simplifying x = -0.150709795Subproblem 2
x + 16 = -15.849290205 Simplifying x + 16 = -15.849290205 Reorder the terms: 16 + x = -15.849290205 Solving 16 + x = -15.849290205 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 = -15.849290205 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.849290205 + -16 x = -15.849290205 + -16 Combine like terms: -15.849290205 + -16 = -31.849290205 x = -31.849290205 Simplifying x = -31.849290205Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.150709795, -31.849290205}
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