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Simplifying (50 + -2x)(25x + 400) = 204000 Reorder the terms: (50 + -2x)(400 + 25x) = 204000 Multiply (50 + -2x) * (400 + 25x) (50(400 + 25x) + -2x * (400 + 25x)) = 204000 ((400 * 50 + 25x * 50) + -2x * (400 + 25x)) = 204000 ((20000 + 1250x) + -2x * (400 + 25x)) = 204000 (20000 + 1250x + (400 * -2x + 25x * -2x)) = 204000 (20000 + 1250x + (-800x + -50x2)) = 204000 Combine like terms: 1250x + -800x = 450x (20000 + 450x + -50x2) = 204000 Solving 20000 + 450x + -50x2 = 204000 Solving for variable 'x'. Reorder the terms: 20000 + -204000 + 450x + -50x2 = 204000 + -204000 Combine like terms: 20000 + -204000 = -184000 -184000 + 450x + -50x2 = 204000 + -204000 Combine like terms: 204000 + -204000 = 0 -184000 + 450x + -50x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-3680 + 9x + -1x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-3680 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying -3680 + 9x + -1x2 = 0 Solving -3680 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3680 + -9x + x2 = 0 Move the constant term to the right: Add '-3680' to each side of the equation. 3680 + -9x + -3680 + x2 = 0 + -3680 Reorder the terms: 3680 + -3680 + -9x + x2 = 0 + -3680 Combine like terms: 3680 + -3680 = 0 0 + -9x + x2 = 0 + -3680 -9x + x2 = 0 + -3680 Combine like terms: 0 + -3680 = -3680 -9x + x2 = -3680 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -3680 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -3680 + 20.25 Combine like terms: -3680 + 20.25 = -3659.75 20.25 + -9x + x2 = -3659.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -3659.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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