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Simplifying 15x2 + 16x + 3 = 0 Reorder the terms: 3 + 16x + 15x2 = 0 Solving 3 + 16x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.2 + 1.066666667x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.066666667x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.066666667x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.066666667x + x2 = 0 + -0.2 1.066666667x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.066666667x + x2 = -0.2 The x term is 1.066666667x. Take half its coefficient (0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. 1.066666667x + 0.2844444446 + x2 = -0.2 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667x + x2 = -0.2 + 0.2844444446 Combine like terms: -0.2 + 0.2844444446 = 0.0844444446 0.2844444446 + 1.066666667x + x2 = 0.0844444446 Factor a perfect square on the left side: (x + 0.5333333335)(x + 0.5333333335) = 0.0844444446 Calculate the square root of the right side: 0.290593263 Break this problem into two subproblems by setting (x + 0.5333333335) equal to 0.290593263 and -0.290593263.Subproblem 1
x + 0.5333333335 = 0.290593263 Simplifying x + 0.5333333335 = 0.290593263 Reorder the terms: 0.5333333335 + x = 0.290593263 Solving 0.5333333335 + x = 0.290593263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = 0.290593263 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = 0.290593263 + -0.5333333335 x = 0.290593263 + -0.5333333335 Combine like terms: 0.290593263 + -0.5333333335 = -0.2427400705 x = -0.2427400705 Simplifying x = -0.2427400705Subproblem 2
x + 0.5333333335 = -0.290593263 Simplifying x + 0.5333333335 = -0.290593263 Reorder the terms: 0.5333333335 + x = -0.290593263 Solving 0.5333333335 + x = -0.290593263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = -0.290593263 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = -0.290593263 + -0.5333333335 x = -0.290593263 + -0.5333333335 Combine like terms: -0.290593263 + -0.5333333335 = -0.8239265965 x = -0.8239265965 Simplifying x = -0.8239265965Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2427400705, -0.8239265965}
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