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Simplifying 0.375 + -0.875X + 0.5X2 = 0 Solving 0.375 + -0.875X + 0.5X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 0.75 + -1.75X + X2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1.75X + -0.75 + X2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1.75X + X2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1.75X + X2 = 0 + -0.75 -1.75X + X2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1.75X + X2 = -0.75 The X term is -1.75X. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75X + 0.765625 + X2 = -0.75 + 0.765625 Reorder the terms: 0.765625 + -1.75X + X2 = -0.75 + 0.765625 Combine like terms: -0.75 + 0.765625 = 0.015625 0.765625 + -1.75X + X2 = 0.015625 Factor a perfect square on the left side: (X + -0.875)(X + -0.875) = 0.015625 Calculate the square root of the right side: 0.125 Break this problem into two subproblems by setting (X + -0.875) equal to 0.125 and -0.125.Subproblem 1
X + -0.875 = 0.125 Simplifying X + -0.875 = 0.125 Reorder the terms: -0.875 + X = 0.125 Solving -0.875 + X = 0.125 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + X = 0.125 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + X = 0.125 + 0.875 X = 0.125 + 0.875 Combine like terms: 0.125 + 0.875 = 1 X = 1 Simplifying X = 1Subproblem 2
X + -0.875 = -0.125 Simplifying X + -0.875 = -0.125 Reorder the terms: -0.875 + X = -0.125 Solving -0.875 + X = -0.125 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + X = -0.125 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + X = -0.125 + 0.875 X = -0.125 + 0.875 Combine like terms: -0.125 + 0.875 = 0.75 X = 0.75 Simplifying X = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. X = {1, 0.75}
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