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Simplifying (2x + 7)(x) = 260 Reorder the terms: (7 + 2x)(x) = 260 Reorder the terms for easier multiplication: x(7 + 2x) = 260 (7 * x + 2x * x) = 260 (7x + 2x2) = 260 Solving 7x + 2x2 = 260 Solving for variable 'x'. Reorder the terms: -260 + 7x + 2x2 = 260 + -260 Combine like terms: 260 + -260 = 0 -260 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -130 + 3.5x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 3.5x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 3.5x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 3.5x + x2 = 0 + 130 3.5x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 3.5x + x2 = 130 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 = 130 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 130 + 3.0625 Combine like terms: 130 + 3.0625 = 133.0625 3.0625 + 3.5x + x2 = 133.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 133.0625 Calculate the square root of the right side: 11.535271995 Break this problem into two subproblems by setting (x + 1.75) equal to 11.535271995 and -11.535271995.Subproblem 1
x + 1.75 = 11.535271995 Simplifying x + 1.75 = 11.535271995 Reorder the terms: 1.75 + x = 11.535271995 Solving 1.75 + x = 11.535271995 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 = 11.535271995 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 11.535271995 + -1.75 x = 11.535271995 + -1.75 Combine like terms: 11.535271995 + -1.75 = 9.785271995 x = 9.785271995 Simplifying x = 9.785271995Subproblem 2
x + 1.75 = -11.535271995 Simplifying x + 1.75 = -11.535271995 Reorder the terms: 1.75 + x = -11.535271995 Solving 1.75 + x = -11.535271995 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 = -11.535271995 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -11.535271995 + -1.75 x = -11.535271995 + -1.75 Combine like terms: -11.535271995 + -1.75 = -13.285271995 x = -13.285271995 Simplifying x = -13.285271995Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.785271995, -13.285271995}
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