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Simplifying (2x)(x + 2) = 144 Remove parenthesis around (2x) 2x(x + 2) = 144 Reorder the terms: 2x(2 + x) = 144 (2 * 2x + x * 2x) = 144 (4x + 2x2) = 144 Solving 4x + 2x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 4x + 2x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + 2x + x2)' equal to zero and attempt to solve: Simplifying -72 + 2x + x2 = 0 Solving -72 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 2x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 2x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 2x + x2 = 0 + 72 2x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 2x + x2 = 72 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 72 + 1 Reorder the terms: 1 + 2x + x2 = 72 + 1 Combine like terms: 72 + 1 = 73 1 + 2x + x2 = 73 Factor a perfect square on the left side: (x + 1)(x + 1) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 1) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 1 = 8.544003745 Simplifying x + 1 = 8.544003745 Reorder the terms: 1 + x = 8.544003745 Solving 1 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.544003745 + -1 x = 8.544003745 + -1 Combine like terms: 8.544003745 + -1 = 7.544003745 x = 7.544003745 Simplifying x = 7.544003745Subproblem 2
x + 1 = -8.544003745 Simplifying x + 1 = -8.544003745 Reorder the terms: 1 + x = -8.544003745 Solving 1 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.544003745 + -1 x = -8.544003745 + -1 Combine like terms: -8.544003745 + -1 = -9.544003745 x = -9.544003745 Simplifying x = -9.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.544003745, -9.544003745}Solution
x = {7.544003745, -9.544003745}
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