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Simplifying x2 + 0.35x + -0.0625 = 0 Reorder the terms: -0.0625 + 0.35x + x2 = 0 Solving -0.0625 + 0.35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.35x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.35x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.35x + x2 = 0 + 0.0625 0.35x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.35x + x2 = 0.0625 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 0.0625 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.0625 + 0.030625 Combine like terms: 0.0625 + 0.030625 = 0.093125 0.030625 + 0.35x + x2 = 0.093125 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 0.093125 Calculate the square root of the right side: 0.30516389 Break this problem into two subproblems by setting (x + 0.175) equal to 0.30516389 and -0.30516389.Subproblem 1
x + 0.175 = 0.30516389 Simplifying x + 0.175 = 0.30516389 Reorder the terms: 0.175 + x = 0.30516389 Solving 0.175 + x = 0.30516389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 0.30516389 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.30516389 + -0.175 x = 0.30516389 + -0.175 Combine like terms: 0.30516389 + -0.175 = 0.13016389 x = 0.13016389 Simplifying x = 0.13016389Subproblem 2
x + 0.175 = -0.30516389 Simplifying x + 0.175 = -0.30516389 Reorder the terms: 0.175 + x = -0.30516389 Solving 0.175 + x = -0.30516389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -0.30516389 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.30516389 + -0.175 x = -0.30516389 + -0.175 Combine like terms: -0.30516389 + -0.175 = -0.48016389 x = -0.48016389 Simplifying x = -0.48016389Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13016389, -0.48016389}
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