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Simplifying X2 = 23X + -30 Reorder the terms: X2 = -30 + 23X Solving X2 = -30 + 23X Solving for variable 'X'. Reorder the terms: 30 + -23X + X2 = -30 + 23X + 30 + -23X Reorder the terms: 30 + -23X + X2 = -30 + 30 + 23X + -23X Combine like terms: -30 + 30 = 0 30 + -23X + X2 = 0 + 23X + -23X 30 + -23X + X2 = 23X + -23X Combine like terms: 23X + -23X = 0 30 + -23X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -23X + -30 + X2 = 0 + -30 Reorder the terms: 30 + -30 + -23X + X2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -23X + X2 = 0 + -30 -23X + X2 = 0 + -30 Combine like terms: 0 + -30 = -30 -23X + X2 = -30 The X term is -23X. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23X + 132.25 + X2 = -30 + 132.25 Reorder the terms: 132.25 + -23X + X2 = -30 + 132.25 Combine like terms: -30 + 132.25 = 102.25 132.25 + -23X + X2 = 102.25 Factor a perfect square on the left side: (X + -11.5)(X + -11.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (X + -11.5) equal to 10.111874208 and -10.111874208.Subproblem 1
X + -11.5 = 10.111874208 Simplifying X + -11.5 = 10.111874208 Reorder the terms: -11.5 + X = 10.111874208 Solving -11.5 + X = 10.111874208 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + X = 10.111874208 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + X = 10.111874208 + 11.5 X = 10.111874208 + 11.5 Combine like terms: 10.111874208 + 11.5 = 21.611874208 X = 21.611874208 Simplifying X = 21.611874208Subproblem 2
X + -11.5 = -10.111874208 Simplifying X + -11.5 = -10.111874208 Reorder the terms: -11.5 + X = -10.111874208 Solving -11.5 + X = -10.111874208 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + X = -10.111874208 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + X = -10.111874208 + 11.5 X = -10.111874208 + 11.5 Combine like terms: -10.111874208 + 11.5 = 1.388125792 X = 1.388125792 Simplifying X = 1.388125792Solution
The solution to the problem is based on the solutions from the subproblems. X = {21.611874208, 1.388125792}
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