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Simplifying 2x2 + -12x = 16 Reorder the terms: -12x + 2x2 = 16 Solving -12x + 2x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -12x + 2x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -6x + x2)' equal to zero and attempt to solve: Simplifying -8 + -6x + x2 = 0 Solving -8 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6x + x2 = 0 + 8 -6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6x + x2 = 8 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 = 8 + 9 Reorder the terms: 9 + -6x + x2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6x + x2 = 17 Factor a perfect square on the left side: (x + -3)(x + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -3 = 4.123105626 Simplifying x + -3 = 4.123105626 Reorder the terms: -3 + x = 4.123105626 Solving -3 + x = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.123105626 + 3 x = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 x = 7.123105626 Simplifying x = 7.123105626Subproblem 2
x + -3 = -4.123105626 Simplifying x + -3 = -4.123105626 Reorder the terms: -3 + x = -4.123105626 Solving -3 + x = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.123105626 + 3 x = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 x = -1.123105626 Simplifying x = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.123105626, -1.123105626}Solution
x = {7.123105626, -1.123105626}
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