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Simplifying 335(x2) + 180x + -64 = 0 Reorder the terms: -64 + 180x + 335x2 = 0 Solving -64 + 180x + 335x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 335 the coefficient of the squared term: Divide each side by '335'. -0.1910447761 + 0.5373134328x + x2 = 0 Move the constant term to the right: Add '0.1910447761' to each side of the equation. -0.1910447761 + 0.5373134328x + 0.1910447761 + x2 = 0 + 0.1910447761 Reorder the terms: -0.1910447761 + 0.1910447761 + 0.5373134328x + x2 = 0 + 0.1910447761 Combine like terms: -0.1910447761 + 0.1910447761 = 0.0000000000 0.0000000000 + 0.5373134328x + x2 = 0 + 0.1910447761 0.5373134328x + x2 = 0 + 0.1910447761 Combine like terms: 0 + 0.1910447761 = 0.1910447761 0.5373134328x + x2 = 0.1910447761 The x term is 0.5373134328x. Take half its coefficient (0.2686567164). Square it (0.07217643127) and add it to both sides. Add '0.07217643127' to each side of the equation. 0.5373134328x + 0.07217643127 + x2 = 0.1910447761 + 0.07217643127 Reorder the terms: 0.07217643127 + 0.5373134328x + x2 = 0.1910447761 + 0.07217643127 Combine like terms: 0.1910447761 + 0.07217643127 = 0.26322120737 0.07217643127 + 0.5373134328x + x2 = 0.26322120737 Factor a perfect square on the left side: (x + 0.2686567164)(x + 0.2686567164) = 0.26322120737 Calculate the square root of the right side: 0.513050882 Break this problem into two subproblems by setting (x + 0.2686567164) equal to 0.513050882 and -0.513050882.Subproblem 1
x + 0.2686567164 = 0.513050882 Simplifying x + 0.2686567164 = 0.513050882 Reorder the terms: 0.2686567164 + x = 0.513050882 Solving 0.2686567164 + x = 0.513050882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2686567164' to each side of the equation. 0.2686567164 + -0.2686567164 + x = 0.513050882 + -0.2686567164 Combine like terms: 0.2686567164 + -0.2686567164 = 0.0000000000 0.0000000000 + x = 0.513050882 + -0.2686567164 x = 0.513050882 + -0.2686567164 Combine like terms: 0.513050882 + -0.2686567164 = 0.2443941656 x = 0.2443941656 Simplifying x = 0.2443941656Subproblem 2
x + 0.2686567164 = -0.513050882 Simplifying x + 0.2686567164 = -0.513050882 Reorder the terms: 0.2686567164 + x = -0.513050882 Solving 0.2686567164 + x = -0.513050882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2686567164' to each side of the equation. 0.2686567164 + -0.2686567164 + x = -0.513050882 + -0.2686567164 Combine like terms: 0.2686567164 + -0.2686567164 = 0.0000000000 0.0000000000 + x = -0.513050882 + -0.2686567164 x = -0.513050882 + -0.2686567164 Combine like terms: -0.513050882 + -0.2686567164 = -0.7817075984 x = -0.7817075984 Simplifying x = -0.7817075984Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2443941656, -0.7817075984}
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