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Simplifying x2 + 12x = 324 Reorder the terms: 12x + x2 = 324 Solving 12x + x2 = 324 Solving for variable 'x'. Reorder the terms: -324 + 12x + x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -324 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 12x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 12x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 12x + x2 = 0 + 324 12x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 12x + x2 = 324 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 = 324 + 36 Reorder the terms: 36 + 12x + x2 = 324 + 36 Combine like terms: 324 + 36 = 360 36 + 12x + x2 = 360 Factor a perfect square on the left side: (x + 6)(x + 6) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (x + 6) equal to 18.973665961 and -18.973665961.Subproblem 1
x + 6 = 18.973665961 Simplifying x + 6 = 18.973665961 Reorder the terms: 6 + x = 18.973665961 Solving 6 + x = 18.973665961 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 = 18.973665961 + -6 Combine like terms: 6 + -6 = 0 0 + x = 18.973665961 + -6 x = 18.973665961 + -6 Combine like terms: 18.973665961 + -6 = 12.973665961 x = 12.973665961 Simplifying x = 12.973665961Subproblem 2
x + 6 = -18.973665961 Simplifying x + 6 = -18.973665961 Reorder the terms: 6 + x = -18.973665961 Solving 6 + x = -18.973665961 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 = -18.973665961 + -6 Combine like terms: 6 + -6 = 0 0 + x = -18.973665961 + -6 x = -18.973665961 + -6 Combine like terms: -18.973665961 + -6 = -24.973665961 x = -24.973665961 Simplifying x = -24.973665961Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.973665961, -24.973665961}
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