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Simplifying x(45 + -1x) = 9 (45 * x + -1x * x) = 9 (45x + -1x2) = 9 Solving 45x + -1x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 45x + -1x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 45x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -45x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -45x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -45x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -45x + x2 = 0 + -9 -45x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -45x + x2 = -9 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -9 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -9 + 506.25 Combine like terms: -9 + 506.25 = 497.25 506.25 + -45x + x2 = 497.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 497.25 Calculate the square root of the right side: 22.299103121 Break this problem into two subproblems by setting (x + -22.5) equal to 22.299103121 and -22.299103121.Subproblem 1
x + -22.5 = 22.299103121 Simplifying x + -22.5 = 22.299103121 Reorder the terms: -22.5 + x = 22.299103121 Solving -22.5 + x = 22.299103121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 22.299103121 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 22.299103121 + 22.5 x = 22.299103121 + 22.5 Combine like terms: 22.299103121 + 22.5 = 44.799103121 x = 44.799103121 Simplifying x = 44.799103121Subproblem 2
x + -22.5 = -22.299103121 Simplifying x + -22.5 = -22.299103121 Reorder the terms: -22.5 + x = -22.299103121 Solving -22.5 + x = -22.299103121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -22.299103121 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -22.299103121 + 22.5 x = -22.299103121 + 22.5 Combine like terms: -22.299103121 + 22.5 = 0.200896879 x = 0.200896879 Simplifying x = 0.200896879Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.799103121, 0.200896879}
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