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Simplifying 2x2 + x = 352 Reorder the terms: x + 2x2 = 352 Solving x + 2x2 = 352 Solving for variable 'x'. Reorder the terms: -352 + x + 2x2 = 352 + -352 Combine like terms: 352 + -352 = 0 -352 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -176 + 0.5x + x2 = 0 Move the constant term to the right: Add '176' to each side of the equation. -176 + 0.5x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + 0.5x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + 0.5x + x2 = 0 + 176 0.5x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 0.5x + x2 = 176 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. 0.5x + 0.25 + x2 = 176 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 176 + 0.25 Combine like terms: 176 + 0.25 = 176.25 0.25 + 0.5x + x2 = 176.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (x + 0.5) equal to 13.275918047 and -13.275918047.Subproblem 1
x + 0.5 = 13.275918047 Simplifying x + 0.5 = 13.275918047 Reorder the terms: 0.5 + x = 13.275918047 Solving 0.5 + x = 13.275918047 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 = 13.275918047 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.275918047 + -0.5 x = 13.275918047 + -0.5 Combine like terms: 13.275918047 + -0.5 = 12.775918047 x = 12.775918047 Simplifying x = 12.775918047Subproblem 2
x + 0.5 = -13.275918047 Simplifying x + 0.5 = -13.275918047 Reorder the terms: 0.5 + x = -13.275918047 Solving 0.5 + x = -13.275918047 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 = -13.275918047 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.275918047 + -0.5 x = -13.275918047 + -0.5 Combine like terms: -13.275918047 + -0.5 = -13.775918047 x = -13.775918047 Simplifying x = -13.775918047Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.775918047, -13.775918047}
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