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Simplifying (4.77(X + -80))(0.808(X + -25)) = 0 Reorder the terms: (4.77(-80 + X))(0.808(X + -25)) = 0 ((-80 * 4.77 + X * 4.77))(0.808(X + -25)) = 0 ((-381.6 + 4.77X))(0.808(X + -25)) = 0 Reorder the terms: (-381.6 + 4.77X)(0.808(-25 + X)) = 0 (-381.6 + 4.77X)((-25 * 0.808 + X * 0.808)) = 0 (-381.6 + 4.77X)((-20.2 + 0.808X)) = 0 Multiply (-381.6 + 4.77X) * (-20.2 + 0.808X) (-381.6(-20.2 + 0.808X) + 4.77X * (-20.2 + 0.808X)) = 0 ((-20.2 * -381.6 + 0.808X * -381.6) + 4.77X * (-20.2 + 0.808X)) = 0 ((7708.32 + -308.3328X) + 4.77X * (-20.2 + 0.808X)) = 0 (7708.32 + -308.3328X + (-20.2 * 4.77X + 0.808X * 4.77X)) = 0 (7708.32 + -308.3328X + (-96.354X + 3.85416X2)) = 0 Combine like terms: -308.3328X + -96.354X = -404.6868X (7708.32 + -404.6868X + 3.85416X2) = 0 Solving 7708.32 + -404.6868X + 3.85416X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3.85416 the coefficient of the squared term: Divide each side by '3.85416'. 2000 + -105X + X2 = 0 Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -105X + -2000 + X2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -105X + X2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -105X + X2 = 0 + -2000 -105X + X2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -105X + X2 = -2000 The X term is -105X. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105X + 2756.25 + X2 = -2000 + 2756.25 Reorder the terms: 2756.25 + -105X + X2 = -2000 + 2756.25 Combine like terms: -2000 + 2756.25 = 756.25 2756.25 + -105X + X2 = 756.25 Factor a perfect square on the left side: (X + -52.5)(X + -52.5) = 756.25 Calculate the square root of the right side: 27.5 Break this problem into two subproblems by setting (X + -52.5) equal to 27.5 and -27.5.Subproblem 1
X + -52.5 = 27.5 Simplifying X + -52.5 = 27.5 Reorder the terms: -52.5 + X = 27.5 Solving -52.5 + X = 27.5 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + X = 27.5 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + X = 27.5 + 52.5 X = 27.5 + 52.5 Combine like terms: 27.5 + 52.5 = 80 X = 80 Simplifying X = 80Subproblem 2
X + -52.5 = -27.5 Simplifying X + -52.5 = -27.5 Reorder the terms: -52.5 + X = -27.5 Solving -52.5 + X = -27.5 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + X = -27.5 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + X = -27.5 + 52.5 X = -27.5 + 52.5 Combine like terms: -27.5 + 52.5 = 25 X = 25 Simplifying X = 25Solution
The solution to the problem is based on the solutions from the subproblems. X = {80, 25}
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