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Simplifying 12x2 + 144x = 1728 Reorder the terms: 144x + 12x2 = 1728 Solving 144x + 12x2 = 1728 Solving for variable 'x'. Reorder the terms: -1728 + 144x + 12x2 = 1728 + -1728 Combine like terms: 1728 + -1728 = 0 -1728 + 144x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-144 + 12x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-144 + 12x + x2)' equal to zero and attempt to solve: Simplifying -144 + 12x + x2 = 0 Solving -144 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 12x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 12x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 12x + x2 = 0 + 144 12x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 12x + x2 = 144 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 = 144 + 36 Reorder the terms: 36 + 12x + x2 = 144 + 36 Combine like terms: 144 + 36 = 180 36 + 12x + x2 = 180 Factor a perfect square on the left side: (x + 6)(x + 6) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + 6) equal to 13.416407865 and -13.416407865.Subproblem 1
x + 6 = 13.416407865 Simplifying x + 6 = 13.416407865 Reorder the terms: 6 + x = 13.416407865 Solving 6 + x = 13.416407865 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 = 13.416407865 + -6 Combine like terms: 6 + -6 = 0 0 + x = 13.416407865 + -6 x = 13.416407865 + -6 Combine like terms: 13.416407865 + -6 = 7.416407865 x = 7.416407865 Simplifying x = 7.416407865Subproblem 2
x + 6 = -13.416407865 Simplifying x + 6 = -13.416407865 Reorder the terms: 6 + x = -13.416407865 Solving 6 + x = -13.416407865 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 = -13.416407865 + -6 Combine like terms: 6 + -6 = 0 0 + x = -13.416407865 + -6 x = -13.416407865 + -6 Combine like terms: -13.416407865 + -6 = -19.416407865 x = -19.416407865 Simplifying x = -19.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.416407865, -19.416407865}Solution
x = {7.416407865, -19.416407865}
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