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Simplifying -1X * X + 40X = 20 Multiply X * X -1X2 + 40X = 20 Reorder the terms: 40X + -1X2 = 20 Solving 40X + -1X2 = 20 Solving for variable 'X'. Reorder the terms: -20 + 40X + -1X2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 40X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -40X + X2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -40X + -20 + X2 = 0 + -20 Reorder the terms: 20 + -20 + -40X + X2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -40X + X2 = 0 + -20 -40X + X2 = 0 + -20 Combine like terms: 0 + -20 = -20 -40X + X2 = -20 The X term is -40X. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40X + 400 + X2 = -20 + 400 Reorder the terms: 400 + -40X + X2 = -20 + 400 Combine like terms: -20 + 400 = 380 400 + -40X + X2 = 380 Factor a perfect square on the left side: (X + -20)(X + -20) = 380 Calculate the square root of the right side: 19.49358869 Break this problem into two subproblems by setting (X + -20) equal to 19.49358869 and -19.49358869.Subproblem 1
X + -20 = 19.49358869 Simplifying X + -20 = 19.49358869 Reorder the terms: -20 + X = 19.49358869 Solving -20 + X = 19.49358869 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + X = 19.49358869 + 20 Combine like terms: -20 + 20 = 0 0 + X = 19.49358869 + 20 X = 19.49358869 + 20 Combine like terms: 19.49358869 + 20 = 39.49358869 X = 39.49358869 Simplifying X = 39.49358869Subproblem 2
X + -20 = -19.49358869 Simplifying X + -20 = -19.49358869 Reorder the terms: -20 + X = -19.49358869 Solving -20 + X = -19.49358869 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + X = -19.49358869 + 20 Combine like terms: -20 + 20 = 0 0 + X = -19.49358869 + 20 X = -19.49358869 + 20 Combine like terms: -19.49358869 + 20 = 0.50641131 X = 0.50641131 Simplifying X = 0.50641131Solution
The solution to the problem is based on the solutions from the subproblems. X = {39.49358869, 0.50641131}
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