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Simplifying (2x) * x + (12) * x + -1560 = 0 Remove parenthesis around (2x) 2x * x + (12) * x + -1560 = 0 Multiply x * x 2x2 + (12) * x + -1560 = 0 Reorder the terms: -1560 + 12x + 2x2 = 0 Solving -1560 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-780 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-780 + 6x + x2)' equal to zero and attempt to solve: Simplifying -780 + 6x + x2 = 0 Solving -780 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '780' to each side of the equation. -780 + 6x + 780 + x2 = 0 + 780 Reorder the terms: -780 + 780 + 6x + x2 = 0 + 780 Combine like terms: -780 + 780 = 0 0 + 6x + x2 = 0 + 780 6x + x2 = 0 + 780 Combine like terms: 0 + 780 = 780 6x + x2 = 780 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 780 + 9 Reorder the terms: 9 + 6x + x2 = 780 + 9 Combine like terms: 780 + 9 = 789 9 + 6x + x2 = 789 Factor a perfect square on the left side: (x + 3)(x + 3) = 789 Calculate the square root of the right side: 28.08914381 Break this problem into two subproblems by setting (x + 3) equal to 28.08914381 and -28.08914381.Subproblem 1
x + 3 = 28.08914381 Simplifying x + 3 = 28.08914381 Reorder the terms: 3 + x = 28.08914381 Solving 3 + x = 28.08914381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 28.08914381 + -3 Combine like terms: 3 + -3 = 0 0 + x = 28.08914381 + -3 x = 28.08914381 + -3 Combine like terms: 28.08914381 + -3 = 25.08914381 x = 25.08914381 Simplifying x = 25.08914381Subproblem 2
x + 3 = -28.08914381 Simplifying x + 3 = -28.08914381 Reorder the terms: 3 + x = -28.08914381 Solving 3 + x = -28.08914381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -28.08914381 + -3 Combine like terms: 3 + -3 = 0 0 + x = -28.08914381 + -3 x = -28.08914381 + -3 Combine like terms: -28.08914381 + -3 = -31.08914381 x = -31.08914381 Simplifying x = -31.08914381Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.08914381, -31.08914381}Solution
x = {25.08914381, -31.08914381}
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