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Simplifying 3x2 + x + -442 = 0 Reorder the terms: -442 + x + 3x2 = 0 Solving -442 + x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -147.3333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '147.3333333' to each side of the equation. -147.3333333 + 0.3333333333x + 147.3333333 + x2 = 0 + 147.3333333 Reorder the terms: -147.3333333 + 147.3333333 + 0.3333333333x + x2 = 0 + 147.3333333 Combine like terms: -147.3333333 + 147.3333333 = 0.0000000 0.0000000 + 0.3333333333x + x2 = 0 + 147.3333333 0.3333333333x + x2 = 0 + 147.3333333 Combine like terms: 0 + 147.3333333 = 147.3333333 0.3333333333x + x2 = 147.3333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 147.3333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 147.3333333 + 0.25 Combine like terms: 147.3333333 + 0.25 = 147.5833333 0.25 + 0.3333333333x + x2 = 147.5833333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 147.5833333 Calculate the square root of the right side: 12.148388095 Break this problem into two subproblems by setting (x + 0.5) equal to 12.148388095 and -12.148388095.Subproblem 1
x + 0.5 = 12.148388095 Simplifying x + 0.5 = 12.148388095 Reorder the terms: 0.5 + x = 12.148388095 Solving 0.5 + x = 12.148388095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.148388095 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.148388095 + -0.5 x = 12.148388095 + -0.5 Combine like terms: 12.148388095 + -0.5 = 11.648388095 x = 11.648388095 Simplifying x = 11.648388095Subproblem 2
x + 0.5 = -12.148388095 Simplifying x + 0.5 = -12.148388095 Reorder the terms: 0.5 + x = -12.148388095 Solving 0.5 + x = -12.148388095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.148388095 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.148388095 + -0.5 x = -12.148388095 + -0.5 Combine like terms: -12.148388095 + -0.5 = -12.648388095 x = -12.648388095 Simplifying x = -12.648388095Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.648388095, -12.648388095}
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