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Simplifying 166 = 7x(x + 6) Reorder the terms: 166 = 7x(6 + x) 166 = (6 * 7x + x * 7x) 166 = (42x + 7x2) Solving 166 = 42x + 7x2 Solving for variable 'x'. Reorder the terms: 166 + -42x + -7x2 = 42x + -42x + 7x2 + -7x2 Combine like terms: 42x + -42x = 0 166 + -42x + -7x2 = 0 + 7x2 + -7x2 166 + -42x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 166 + -42x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -23.71428571 + 6x + x2 = 0 Move the constant term to the right: Add '23.71428571' to each side of the equation. -23.71428571 + 6x + 23.71428571 + x2 = 0 + 23.71428571 Reorder the terms: -23.71428571 + 23.71428571 + 6x + x2 = 0 + 23.71428571 Combine like terms: -23.71428571 + 23.71428571 = 0.00000000 0.00000000 + 6x + x2 = 0 + 23.71428571 6x + x2 = 0 + 23.71428571 Combine like terms: 0 + 23.71428571 = 23.71428571 6x + x2 = 23.71428571 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 23.71428571 + 9 Reorder the terms: 9 + 6x + x2 = 23.71428571 + 9 Combine like terms: 23.71428571 + 9 = 32.71428571 9 + 6x + x2 = 32.71428571 Factor a perfect square on the left side: (x + 3)(x + 3) = 32.71428571 Calculate the square root of the right side: 5.719640348 Break this problem into two subproblems by setting (x + 3) equal to 5.719640348 and -5.719640348.Subproblem 1
x + 3 = 5.719640348 Simplifying x + 3 = 5.719640348 Reorder the terms: 3 + x = 5.719640348 Solving 3 + x = 5.719640348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.719640348 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.719640348 + -3 x = 5.719640348 + -3 Combine like terms: 5.719640348 + -3 = 2.719640348 x = 2.719640348 Simplifying x = 2.719640348Subproblem 2
x + 3 = -5.719640348 Simplifying x + 3 = -5.719640348 Reorder the terms: 3 + x = -5.719640348 Solving 3 + x = -5.719640348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.719640348 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.719640348 + -3 x = -5.719640348 + -3 Combine like terms: -5.719640348 + -3 = -8.719640348 x = -8.719640348 Simplifying x = -8.719640348Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.719640348, -8.719640348}
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