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Simplifying 126 = (10 + (x + 2)) * x + 2 Reorder the terms: 126 = (10 + (2 + x)) * x + 2 Remove parenthesis around (2 + x) 126 = (10 + 2 + x) * x + 2 Combine like terms: 10 + 2 = 12 126 = (12 + x) * x + 2 Reorder the terms for easier multiplication: 126 = x(12 + x) + 2 126 = (12 * x + x * x) + 2 126 = (12x + x2) + 2 Reorder the terms: 126 = 2 + 12x + x2 Solving 126 = 2 + 12x + x2 Solving for variable 'x'. Combine like terms: 126 + -2 = 124 124 + -12x + -1x2 = 2 + 12x + x2 + -2 + -12x + -1x2 Reorder the terms: 124 + -12x + -1x2 = 2 + -2 + 12x + -12x + x2 + -1x2 Combine like terms: 2 + -2 = 0 124 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 124 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 124 + -12x + -1x2 = 0 + x2 + -1x2 124 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 124 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -124 + 12x + x2 = 0 Move the constant term to the right: Add '124' to each side of the equation. -124 + 12x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 12x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 12x + x2 = 0 + 124 12x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 12x + x2 = 124 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 124 + 36 Reorder the terms: 36 + 12x + x2 = 124 + 36 Combine like terms: 124 + 36 = 160 36 + 12x + x2 = 160 Factor a perfect square on the left side: (x + 6)(x + 6) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + 6) equal to 12.649110641 and -12.649110641.Subproblem 1
x + 6 = 12.649110641 Simplifying x + 6 = 12.649110641 Reorder the terms: 6 + x = 12.649110641 Solving 6 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 12.649110641 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.649110641 + -6 x = 12.649110641 + -6 Combine like terms: 12.649110641 + -6 = 6.649110641 x = 6.649110641 Simplifying x = 6.649110641Subproblem 2
x + 6 = -12.649110641 Simplifying x + 6 = -12.649110641 Reorder the terms: 6 + x = -12.649110641 Solving 6 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -12.649110641 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.649110641 + -6 x = -12.649110641 + -6 Combine like terms: -12.649110641 + -6 = -18.649110641 x = -18.649110641 Simplifying x = -18.649110641Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.649110641, -18.649110641}
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