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Simplifying 0 = 4X2 + X + -2 Reorder the terms: 0 = -2 + X + 4X2 Solving 0 = -2 + X + 4X2 Solving for variable 'X'. Combine like terms: 0 + 2 = 2 2 + -1X + -4X2 = -2 + X + 4X2 + 2 + -1X + -4X2 Reorder the terms: 2 + -1X + -4X2 = -2 + 2 + X + -1X + 4X2 + -4X2 Combine like terms: -2 + 2 = 0 2 + -1X + -4X2 = 0 + X + -1X + 4X2 + -4X2 2 + -1X + -4X2 = X + -1X + 4X2 + -4X2 Combine like terms: X + -1X = 0 2 + -1X + -4X2 = 0 + 4X2 + -4X2 2 + -1X + -4X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 2 + -1X + -4X2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + 0.25X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.25X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.25X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.25X + X2 = 0 + 0.5 0.25X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.25X + X2 = 0.5 The X term is 0.25X. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25X + 0.015625 + X2 = 0.5 + 0.015625 Reorder the terms: 0.015625 + 0.25X + X2 = 0.5 + 0.015625 Combine like terms: 0.5 + 0.015625 = 0.515625 0.015625 + 0.25X + X2 = 0.515625 Factor a perfect square on the left side: (X + 0.125)(X + 0.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (X + 0.125) equal to 0.718070331 and -0.718070331.Subproblem 1
X + 0.125 = 0.718070331 Simplifying X + 0.125 = 0.718070331 Reorder the terms: 0.125 + X = 0.718070331 Solving 0.125 + X = 0.718070331 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + X = 0.718070331 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + X = 0.718070331 + -0.125 X = 0.718070331 + -0.125 Combine like terms: 0.718070331 + -0.125 = 0.593070331 X = 0.593070331 Simplifying X = 0.593070331Subproblem 2
X + 0.125 = -0.718070331 Simplifying X + 0.125 = -0.718070331 Reorder the terms: 0.125 + X = -0.718070331 Solving 0.125 + X = -0.718070331 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + X = -0.718070331 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + X = -0.718070331 + -0.125 X = -0.718070331 + -0.125 Combine like terms: -0.718070331 + -0.125 = -0.843070331 X = -0.843070331 Simplifying X = -0.843070331Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.593070331, -0.843070331}
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