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Simplifying 0.175 + -0.175x + -1x2 = 0 Solving 0.175 + -0.175x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.175 + 0.175x + x2 = 0 Move the constant term to the right: Add '0.175' to each side of the equation. -0.175 + 0.175x + 0.175 + x2 = 0 + 0.175 Reorder the terms: -0.175 + 0.175 + 0.175x + x2 = 0 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + 0.175x + x2 = 0 + 0.175 0.175x + x2 = 0 + 0.175 Combine like terms: 0 + 0.175 = 0.175 0.175x + x2 = 0.175 The x term is 0.175x. Take half its coefficient (0.0875). Square it (0.00765625) and add it to both sides. Add '0.00765625' to each side of the equation. 0.175x + 0.00765625 + x2 = 0.175 + 0.00765625 Reorder the terms: 0.00765625 + 0.175x + x2 = 0.175 + 0.00765625 Combine like terms: 0.175 + 0.00765625 = 0.18265625 0.00765625 + 0.175x + x2 = 0.18265625 Factor a perfect square on the left side: (x + 0.0875)(x + 0.0875) = 0.18265625 Calculate the square root of the right side: 0.427383025 Break this problem into two subproblems by setting (x + 0.0875) equal to 0.427383025 and -0.427383025.Subproblem 1
x + 0.0875 = 0.427383025 Simplifying x + 0.0875 = 0.427383025 Reorder the terms: 0.0875 + x = 0.427383025 Solving 0.0875 + x = 0.427383025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0875' to each side of the equation. 0.0875 + -0.0875 + x = 0.427383025 + -0.0875 Combine like terms: 0.0875 + -0.0875 = 0.0000 0.0000 + x = 0.427383025 + -0.0875 x = 0.427383025 + -0.0875 Combine like terms: 0.427383025 + -0.0875 = 0.339883025 x = 0.339883025 Simplifying x = 0.339883025Subproblem 2
x + 0.0875 = -0.427383025 Simplifying x + 0.0875 = -0.427383025 Reorder the terms: 0.0875 + x = -0.427383025 Solving 0.0875 + x = -0.427383025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0875' to each side of the equation. 0.0875 + -0.0875 + x = -0.427383025 + -0.0875 Combine like terms: 0.0875 + -0.0875 = 0.0000 0.0000 + x = -0.427383025 + -0.0875 x = -0.427383025 + -0.0875 Combine like terms: -0.427383025 + -0.0875 = -0.514883025 x = -0.514883025 Simplifying x = -0.514883025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.339883025, -0.514883025}
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