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Simplifying (2x + 7)(x) = 340 Reorder the terms: (7 + 2x)(x) = 340 Reorder the terms for easier multiplication: x(7 + 2x) = 340 (7 * x + 2x * x) = 340 (7x + 2x2) = 340 Solving 7x + 2x2 = 340 Solving for variable 'x'. Reorder the terms: -340 + 7x + 2x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -340 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -170 + 3.5x + x2 = 0 Move the constant term to the right: Add '170' to each side of the equation. -170 + 3.5x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 3.5x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 3.5x + x2 = 0 + 170 3.5x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 3.5x + x2 = 170 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 170 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 170 + 3.0625 Combine like terms: 170 + 3.0625 = 173.0625 3.0625 + 3.5x + x2 = 173.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 173.0625 Calculate the square root of the right side: 13.155322117 Break this problem into two subproblems by setting (x + 1.75) equal to 13.155322117 and -13.155322117.Subproblem 1
x + 1.75 = 13.155322117 Simplifying x + 1.75 = 13.155322117 Reorder the terms: 1.75 + x = 13.155322117 Solving 1.75 + x = 13.155322117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 13.155322117 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 13.155322117 + -1.75 x = 13.155322117 + -1.75 Combine like terms: 13.155322117 + -1.75 = 11.405322117 x = 11.405322117 Simplifying x = 11.405322117Subproblem 2
x + 1.75 = -13.155322117 Simplifying x + 1.75 = -13.155322117 Reorder the terms: 1.75 + x = -13.155322117 Solving 1.75 + x = -13.155322117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -13.155322117 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -13.155322117 + -1.75 x = -13.155322117 + -1.75 Combine like terms: -13.155322117 + -1.75 = -14.905322117 x = -14.905322117 Simplifying x = -14.905322117Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.405322117, -14.905322117}
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