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Simplifying 20x2 + 29x + -6 = 0 Reorder the terms: -6 + 29x + 20x2 = 0 Solving -6 + 29x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.3 + 1.45x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.45x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.45x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.45x + x2 = 0 + 0.3 1.45x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 1.45x + x2 = 0.3 The x term is 1.45x. Take half its coefficient (0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. 1.45x + 0.525625 + x2 = 0.3 + 0.525625 Reorder the terms: 0.525625 + 1.45x + x2 = 0.3 + 0.525625 Combine like terms: 0.3 + 0.525625 = 0.825625 0.525625 + 1.45x + x2 = 0.825625 Factor a perfect square on the left side: (x + 0.725)(x + 0.725) = 0.825625 Calculate the square root of the right side: 0.908639092 Break this problem into two subproblems by setting (x + 0.725) equal to 0.908639092 and -0.908639092.Subproblem 1
x + 0.725 = 0.908639092 Simplifying x + 0.725 = 0.908639092 Reorder the terms: 0.725 + x = 0.908639092 Solving 0.725 + x = 0.908639092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.725' to each side of the equation. 0.725 + -0.725 + x = 0.908639092 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = 0.908639092 + -0.725 x = 0.908639092 + -0.725 Combine like terms: 0.908639092 + -0.725 = 0.183639092 x = 0.183639092 Simplifying x = 0.183639092Subproblem 2
x + 0.725 = -0.908639092 Simplifying x + 0.725 = -0.908639092 Reorder the terms: 0.725 + x = -0.908639092 Solving 0.725 + x = -0.908639092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.725' to each side of the equation. 0.725 + -0.725 + x = -0.908639092 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = -0.908639092 + -0.725 x = -0.908639092 + -0.725 Combine like terms: -0.908639092 + -0.725 = -1.633639092 x = -1.633639092 Simplifying x = -1.633639092Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.183639092, -1.633639092}
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