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Simplifying 2x2 + 12x = 1584 Reorder the terms: 12x + 2x2 = 1584 Solving 12x + 2x2 = 1584 Solving for variable 'x'. Reorder the terms: -1584 + 12x + 2x2 = 1584 + -1584 Combine like terms: 1584 + -1584 = 0 -1584 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-792 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-792 + 6x + x2)' equal to zero and attempt to solve: Simplifying -792 + 6x + x2 = 0 Solving -792 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '792' to each side of the equation. -792 + 6x + 792 + x2 = 0 + 792 Reorder the terms: -792 + 792 + 6x + x2 = 0 + 792 Combine like terms: -792 + 792 = 0 0 + 6x + x2 = 0 + 792 6x + x2 = 0 + 792 Combine like terms: 0 + 792 = 792 6x + x2 = 792 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 = 792 + 9 Reorder the terms: 9 + 6x + x2 = 792 + 9 Combine like terms: 792 + 9 = 801 9 + 6x + x2 = 801 Factor a perfect square on the left side: (x + 3)(x + 3) = 801 Calculate the square root of the right side: 28.301943396 Break this problem into two subproblems by setting (x + 3) equal to 28.301943396 and -28.301943396.Subproblem 1
x + 3 = 28.301943396 Simplifying x + 3 = 28.301943396 Reorder the terms: 3 + x = 28.301943396 Solving 3 + x = 28.301943396 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 = 28.301943396 + -3 Combine like terms: 3 + -3 = 0 0 + x = 28.301943396 + -3 x = 28.301943396 + -3 Combine like terms: 28.301943396 + -3 = 25.301943396 x = 25.301943396 Simplifying x = 25.301943396Subproblem 2
x + 3 = -28.301943396 Simplifying x + 3 = -28.301943396 Reorder the terms: 3 + x = -28.301943396 Solving 3 + x = -28.301943396 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 = -28.301943396 + -3 Combine like terms: 3 + -3 = 0 0 + x = -28.301943396 + -3 x = -28.301943396 + -3 Combine like terms: -28.301943396 + -3 = -31.301943396 x = -31.301943396 Simplifying x = -31.301943396Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.301943396, -31.301943396}Solution
x = {25.301943396, -31.301943396}
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