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Simplifying 2x2 + 12x + -3456 = 0 Reorder the terms: -3456 + 12x + 2x2 = 0 Solving -3456 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1728 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1728 + 6x + x2)' equal to zero and attempt to solve: Simplifying -1728 + 6x + x2 = 0 Solving -1728 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1728' to each side of the equation. -1728 + 6x + 1728 + x2 = 0 + 1728 Reorder the terms: -1728 + 1728 + 6x + x2 = 0 + 1728 Combine like terms: -1728 + 1728 = 0 0 + 6x + x2 = 0 + 1728 6x + x2 = 0 + 1728 Combine like terms: 0 + 1728 = 1728 6x + x2 = 1728 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 = 1728 + 9 Reorder the terms: 9 + 6x + x2 = 1728 + 9 Combine like terms: 1728 + 9 = 1737 9 + 6x + x2 = 1737 Factor a perfect square on the left side: (x + 3)(x + 3) = 1737 Calculate the square root of the right side: 41.677331968 Break this problem into two subproblems by setting (x + 3) equal to 41.677331968 and -41.677331968.Subproblem 1
x + 3 = 41.677331968 Simplifying x + 3 = 41.677331968 Reorder the terms: 3 + x = 41.677331968 Solving 3 + x = 41.677331968 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 = 41.677331968 + -3 Combine like terms: 3 + -3 = 0 0 + x = 41.677331968 + -3 x = 41.677331968 + -3 Combine like terms: 41.677331968 + -3 = 38.677331968 x = 38.677331968 Simplifying x = 38.677331968Subproblem 2
x + 3 = -41.677331968 Simplifying x + 3 = -41.677331968 Reorder the terms: 3 + x = -41.677331968 Solving 3 + x = -41.677331968 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 = -41.677331968 + -3 Combine like terms: 3 + -3 = 0 0 + x = -41.677331968 + -3 x = -41.677331968 + -3 Combine like terms: -41.677331968 + -3 = -44.677331968 x = -44.677331968 Simplifying x = -44.677331968Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.677331968, -44.677331968}Solution
x = {38.677331968, -44.677331968}
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