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Simplifying 0 = -0.0001x2 + -0.0008x + 0.19 Reorder the terms: 0 = 0.19 + -0.0008x + -0.0001x2 Solving 0 = 0.19 + -0.0008x + -0.0001x2 Solving for variable 'x'. Combine like terms: 0 + -0.19 = -0.19 -0.19 + 0.0008x + 0.0001x2 = 0.19 + -0.0008x + -0.0001x2 + -0.19 + 0.0008x + 0.0001x2 Reorder the terms: -0.19 + 0.0008x + 0.0001x2 = 0.19 + -0.19 + -0.0008x + 0.0008x + -0.0001x2 + 0.0001x2 Combine like terms: 0.19 + -0.19 = 0.00 -0.19 + 0.0008x + 0.0001x2 = 0.00 + -0.0008x + 0.0008x + -0.0001x2 + 0.0001x2 -0.19 + 0.0008x + 0.0001x2 = -0.0008x + 0.0008x + -0.0001x2 + 0.0001x2 Combine like terms: -0.0008x + 0.0008x = 0.0000 -0.19 + 0.0008x + 0.0001x2 = 0.0000 + -0.0001x2 + 0.0001x2 -0.19 + 0.0008x + 0.0001x2 = -0.0001x2 + 0.0001x2 Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000 -0.19 + 0.0008x + 0.0001x2 = 0.0000 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -1900 + 8x + x2 = 0 Move the constant term to the right: Add '1900' to each side of the equation. -1900 + 8x + 1900 + x2 = 0 + 1900 Reorder the terms: -1900 + 1900 + 8x + x2 = 0 + 1900 Combine like terms: -1900 + 1900 = 0 0 + 8x + x2 = 0 + 1900 8x + x2 = 0 + 1900 Combine like terms: 0 + 1900 = 1900 8x + x2 = 1900 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 1900 + 16 Reorder the terms: 16 + 8x + x2 = 1900 + 16 Combine like terms: 1900 + 16 = 1916 16 + 8x + x2 = 1916 Factor a perfect square on the left side: (x + 4)(x + 4) = 1916 Calculate the square root of the right side: 43.772137256 Break this problem into two subproblems by setting (x + 4) equal to 43.772137256 and -43.772137256.Subproblem 1
x + 4 = 43.772137256 Simplifying x + 4 = 43.772137256 Reorder the terms: 4 + x = 43.772137256 Solving 4 + x = 43.772137256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 43.772137256 + -4 Combine like terms: 4 + -4 = 0 0 + x = 43.772137256 + -4 x = 43.772137256 + -4 Combine like terms: 43.772137256 + -4 = 39.772137256 x = 39.772137256 Simplifying x = 39.772137256Subproblem 2
x + 4 = -43.772137256 Simplifying x + 4 = -43.772137256 Reorder the terms: 4 + x = -43.772137256 Solving 4 + x = -43.772137256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -43.772137256 + -4 Combine like terms: 4 + -4 = 0 0 + x = -43.772137256 + -4 x = -43.772137256 + -4 Combine like terms: -43.772137256 + -4 = -47.772137256 x = -47.772137256 Simplifying x = -47.772137256Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.772137256, -47.772137256}
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