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Simplifying 2(x + 7) * x = 7 Reorder the terms: 2(7 + x) * x = 7 Reorder the terms for easier multiplication: 2x(7 + x) = 7 (7 * 2x + x * 2x) = 7 (14x + 2x2) = 7 Solving 14x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 14x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 7x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 7x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 7x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 7x + x2 = 0 + 3.5 7x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 7x + x2 = 3.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 3.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 3.5 + 12.25 Combine like terms: 3.5 + 12.25 = 15.75 12.25 + 7x + x2 = 15.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + 3.5) equal to 3.968626967 and -3.968626967.Subproblem 1
x + 3.5 = 3.968626967 Simplifying x + 3.5 = 3.968626967 Reorder the terms: 3.5 + x = 3.968626967 Solving 3.5 + x = 3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.968626967 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.968626967 + -3.5 x = 3.968626967 + -3.5 Combine like terms: 3.968626967 + -3.5 = 0.468626967 x = 0.468626967 Simplifying x = 0.468626967Subproblem 2
x + 3.5 = -3.968626967 Simplifying x + 3.5 = -3.968626967 Reorder the terms: 3.5 + x = -3.968626967 Solving 3.5 + x = -3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.968626967 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.968626967 + -3.5 x = -3.968626967 + -3.5 Combine like terms: -3.968626967 + -3.5 = -7.468626967 x = -7.468626967 Simplifying x = -7.468626967Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.468626967, -7.468626967}
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