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Simplifying x2 + 32x + -48 = 0 Reorder the terms: -48 + 32x + x2 = 0 Solving -48 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 32x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 32x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 32x + x2 = 0 + 48 32x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 32x + x2 = 48 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 = 48 + 256 Reorder the terms: 256 + 32x + x2 = 48 + 256 Combine like terms: 48 + 256 = 304 256 + 32x + x2 = 304 Factor a perfect square on the left side: (x + 16)(x + 16) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (x + 16) equal to 17.435595774 and -17.435595774.Subproblem 1
x + 16 = 17.435595774 Simplifying x + 16 = 17.435595774 Reorder the terms: 16 + x = 17.435595774 Solving 16 + x = 17.435595774 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 = 17.435595774 + -16 Combine like terms: 16 + -16 = 0 0 + x = 17.435595774 + -16 x = 17.435595774 + -16 Combine like terms: 17.435595774 + -16 = 1.435595774 x = 1.435595774 Simplifying x = 1.435595774Subproblem 2
x + 16 = -17.435595774 Simplifying x + 16 = -17.435595774 Reorder the terms: 16 + x = -17.435595774 Solving 16 + x = -17.435595774 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 = -17.435595774 + -16 Combine like terms: 16 + -16 = 0 0 + x = -17.435595774 + -16 x = -17.435595774 + -16 Combine like terms: -17.435595774 + -16 = -33.435595774 x = -33.435595774 Simplifying x = -33.435595774Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.435595774, -33.435595774}
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