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Simplifying (x)(32 + -1x) = 48 (32 * x + -1x * x) = 48 (32x + -1x2) = 48 Solving 32x + -1x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 32x + -1x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 48 + -32x + x2 = 0 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 = 208 256 + -32x + x2 = 208 Factor a perfect square on the left side: (x + -16)(x + -16) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + -16) equal to 14.422205102 and -14.422205102.Subproblem 1
x + -16 = 14.422205102 Simplifying x + -16 = 14.422205102 Reorder the terms: -16 + x = 14.422205102 Solving -16 + x = 14.422205102 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 = 14.422205102 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.422205102 + 16 x = 14.422205102 + 16 Combine like terms: 14.422205102 + 16 = 30.422205102 x = 30.422205102 Simplifying x = 30.422205102Subproblem 2
x + -16 = -14.422205102 Simplifying x + -16 = -14.422205102 Reorder the terms: -16 + x = -14.422205102 Solving -16 + x = -14.422205102 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 = -14.422205102 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.422205102 + 16 x = -14.422205102 + 16 Combine like terms: -14.422205102 + 16 = 1.577794898 x = 1.577794898 Simplifying x = 1.577794898Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.422205102, 1.577794898}
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