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Simplifying 40X2 = 1 + -1X Solving 40X2 = 1 + -1X Solving for variable 'X'. Reorder the terms: -1 + X + 40X2 = 1 + -1X + -1 + X Reorder the terms: -1 + X + 40X2 = 1 + -1 + -1X + X Combine like terms: 1 + -1 = 0 -1 + X + 40X2 = 0 + -1X + X -1 + X + 40X2 = -1X + X Combine like terms: -1X + X = 0 -1 + X + 40X2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.025 + 0.025X + X2 = 0 Move the constant term to the right: Add '0.025' to each side of the equation. -0.025 + 0.025X + 0.025 + X2 = 0 + 0.025 Reorder the terms: -0.025 + 0.025 + 0.025X + X2 = 0 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + 0.025X + X2 = 0 + 0.025 0.025X + X2 = 0 + 0.025 Combine like terms: 0 + 0.025 = 0.025 0.025X + X2 = 0.025 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.025X + 0.25 + X2 = 0.025 + 0.25 Reorder the terms: 0.25 + 0.025X + X2 = 0.025 + 0.25 Combine like terms: 0.025 + 0.25 = 0.275 0.25 + 0.025X + X2 = 0.275 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 0.275 Calculate the square root of the right side: 0.524404424 Break this problem into two subproblems by setting (X + 0.5) equal to 0.524404424 and -0.524404424.Subproblem 1
X + 0.5 = 0.524404424 Simplifying X + 0.5 = 0.524404424 Reorder the terms: 0.5 + X = 0.524404424 Solving 0.5 + X = 0.524404424 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 0.524404424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 0.524404424 + -0.5 X = 0.524404424 + -0.5 Combine like terms: 0.524404424 + -0.5 = 0.024404424 X = 0.024404424 Simplifying X = 0.024404424Subproblem 2
X + 0.5 = -0.524404424 Simplifying X + 0.5 = -0.524404424 Reorder the terms: 0.5 + X = -0.524404424 Solving 0.5 + X = -0.524404424 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -0.524404424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -0.524404424 + -0.5 X = -0.524404424 + -0.5 Combine like terms: -0.524404424 + -0.5 = -1.024404424 X = -1.024404424 Simplifying X = -1.024404424Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.024404424, -1.024404424}
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