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Simplifying 2x2 + 12x + -1040 = 1008 Reorder the terms: -1040 + 12x + 2x2 = 1008 Solving -1040 + 12x + 2x2 = 1008 Solving for variable 'x'. Reorder the terms: -1040 + -1008 + 12x + 2x2 = 1008 + -1008 Combine like terms: -1040 + -1008 = -2048 -2048 + 12x + 2x2 = 1008 + -1008 Combine like terms: 1008 + -1008 = 0 -2048 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1024 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1024 + 6x + x2)' equal to zero and attempt to solve: Simplifying -1024 + 6x + x2 = 0 Solving -1024 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1024' to each side of the equation. -1024 + 6x + 1024 + x2 = 0 + 1024 Reorder the terms: -1024 + 1024 + 6x + x2 = 0 + 1024 Combine like terms: -1024 + 1024 = 0 0 + 6x + x2 = 0 + 1024 6x + x2 = 0 + 1024 Combine like terms: 0 + 1024 = 1024 6x + x2 = 1024 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 = 1024 + 9 Reorder the terms: 9 + 6x + x2 = 1024 + 9 Combine like terms: 1024 + 9 = 1033 9 + 6x + x2 = 1033 Factor a perfect square on the left side: (x + 3)(x + 3) = 1033 Calculate the square root of the right side: 32.14031736 Break this problem into two subproblems by setting (x + 3) equal to 32.14031736 and -32.14031736.Subproblem 1
x + 3 = 32.14031736 Simplifying x + 3 = 32.14031736 Reorder the terms: 3 + x = 32.14031736 Solving 3 + x = 32.14031736 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 = 32.14031736 + -3 Combine like terms: 3 + -3 = 0 0 + x = 32.14031736 + -3 x = 32.14031736 + -3 Combine like terms: 32.14031736 + -3 = 29.14031736 x = 29.14031736 Simplifying x = 29.14031736Subproblem 2
x + 3 = -32.14031736 Simplifying x + 3 = -32.14031736 Reorder the terms: 3 + x = -32.14031736 Solving 3 + x = -32.14031736 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 = -32.14031736 + -3 Combine like terms: 3 + -3 = 0 0 + x = -32.14031736 + -3 x = -32.14031736 + -3 Combine like terms: -32.14031736 + -3 = -35.14031736 x = -35.14031736 Simplifying x = -35.14031736Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.14031736, -35.14031736}Solution
x = {29.14031736, -35.14031736}
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