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Simplifying 12x + x2 = 130 Solving 12x + x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + 12x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 12x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 12x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 12x + x2 = 0 + 130 12x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 12x + x2 = 130 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 = 130 + 36 Reorder the terms: 36 + 12x + x2 = 130 + 36 Combine like terms: 130 + 36 = 166 36 + 12x + x2 = 166 Factor a perfect square on the left side: (x + 6)(x + 6) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 6) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 6 = 12.884098727 Simplifying x + 6 = 12.884098727 Reorder the terms: 6 + x = 12.884098727 Solving 6 + x = 12.884098727 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 = 12.884098727 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.884098727 + -6 x = 12.884098727 + -6 Combine like terms: 12.884098727 + -6 = 6.884098727 x = 6.884098727 Simplifying x = 6.884098727Subproblem 2
x + 6 = -12.884098727 Simplifying x + 6 = -12.884098727 Reorder the terms: 6 + x = -12.884098727 Solving 6 + x = -12.884098727 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 = -12.884098727 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.884098727 + -6 x = -12.884098727 + -6 Combine like terms: -12.884098727 + -6 = -18.884098727 x = -18.884098727 Simplifying x = -18.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.884098727, -18.884098727}
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