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Simplifying 20x2 + 29x + -5 = 56 Reorder the terms: -5 + 29x + 20x2 = 56 Solving -5 + 29x + 20x2 = 56 Solving for variable 'x'. Reorder the terms: -5 + -56 + 29x + 20x2 = 56 + -56 Combine like terms: -5 + -56 = -61 -61 + 29x + 20x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -61 + 29x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -3.05 + 1.45x + x2 = 0 Move the constant term to the right: Add '3.05' to each side of the equation. -3.05 + 1.45x + 3.05 + x2 = 0 + 3.05 Reorder the terms: -3.05 + 3.05 + 1.45x + x2 = 0 + 3.05 Combine like terms: -3.05 + 3.05 = 0.00 0.00 + 1.45x + x2 = 0 + 3.05 1.45x + x2 = 0 + 3.05 Combine like terms: 0 + 3.05 = 3.05 1.45x + x2 = 3.05 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 = 3.05 + 0.525625 Reorder the terms: 0.525625 + 1.45x + x2 = 3.05 + 0.525625 Combine like terms: 3.05 + 0.525625 = 3.575625 0.525625 + 1.45x + x2 = 3.575625 Factor a perfect square on the left side: (x + 0.725)(x + 0.725) = 3.575625 Calculate the square root of the right side: 1.89093231 Break this problem into two subproblems by setting (x + 0.725) equal to 1.89093231 and -1.89093231.Subproblem 1
x + 0.725 = 1.89093231 Simplifying x + 0.725 = 1.89093231 Reorder the terms: 0.725 + x = 1.89093231 Solving 0.725 + x = 1.89093231 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 = 1.89093231 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = 1.89093231 + -0.725 x = 1.89093231 + -0.725 Combine like terms: 1.89093231 + -0.725 = 1.16593231 x = 1.16593231 Simplifying x = 1.16593231Subproblem 2
x + 0.725 = -1.89093231 Simplifying x + 0.725 = -1.89093231 Reorder the terms: 0.725 + x = -1.89093231 Solving 0.725 + x = -1.89093231 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 = -1.89093231 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = -1.89093231 + -0.725 x = -1.89093231 + -0.725 Combine like terms: -1.89093231 + -0.725 = -2.61593231 x = -2.61593231 Simplifying x = -2.61593231Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16593231, -2.61593231}
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