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Simplifying x(45 + -0.5x) = 195.5 (45 * x + -0.5x * x) = 195.5 (45x + -0.5x2) = 195.5 Solving 45x + -0.5x2 = 195.5 Solving for variable 'x'. Reorder the terms: -195.5 + 45x + -0.5x2 = 195.5 + -195.5 Combine like terms: 195.5 + -195.5 = 0.0 -195.5 + 45x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 391 + -90x + x2 = 0 Move the constant term to the right: Add '-391' to each side of the equation. 391 + -90x + -391 + x2 = 0 + -391 Reorder the terms: 391 + -391 + -90x + x2 = 0 + -391 Combine like terms: 391 + -391 = 0 0 + -90x + x2 = 0 + -391 -90x + x2 = 0 + -391 Combine like terms: 0 + -391 = -391 -90x + x2 = -391 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -391 + 2025 Reorder the terms: 2025 + -90x + x2 = -391 + 2025 Combine like terms: -391 + 2025 = 1634 2025 + -90x + x2 = 1634 Factor a perfect square on the left side: (x + -45)(x + -45) = 1634 Calculate the square root of the right side: 40.422765863 Break this problem into two subproblems by setting (x + -45) equal to 40.422765863 and -40.422765863.Subproblem 1
x + -45 = 40.422765863 Simplifying x + -45 = 40.422765863 Reorder the terms: -45 + x = 40.422765863 Solving -45 + x = 40.422765863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 40.422765863 + 45 Combine like terms: -45 + 45 = 0 0 + x = 40.422765863 + 45 x = 40.422765863 + 45 Combine like terms: 40.422765863 + 45 = 85.422765863 x = 85.422765863 Simplifying x = 85.422765863Subproblem 2
x + -45 = -40.422765863 Simplifying x + -45 = -40.422765863 Reorder the terms: -45 + x = -40.422765863 Solving -45 + x = -40.422765863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -40.422765863 + 45 Combine like terms: -45 + 45 = 0 0 + x = -40.422765863 + 45 x = -40.422765863 + 45 Combine like terms: -40.422765863 + 45 = 4.577234137 x = 4.577234137 Simplifying x = 4.577234137Solution
The solution to the problem is based on the solutions from the subproblems. x = {85.422765863, 4.577234137}
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