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Simplifying 2x2 + -12x = 936 Reorder the terms: -12x + 2x2 = 936 Solving -12x + 2x2 = 936 Solving for variable 'x'. Reorder the terms: -936 + -12x + 2x2 = 936 + -936 Combine like terms: 936 + -936 = 0 -936 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-468 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-468 + -6x + x2)' equal to zero and attempt to solve: Simplifying -468 + -6x + x2 = 0 Solving -468 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '468' to each side of the equation. -468 + -6x + 468 + x2 = 0 + 468 Reorder the terms: -468 + 468 + -6x + x2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + -6x + x2 = 0 + 468 -6x + x2 = 0 + 468 Combine like terms: 0 + 468 = 468 -6x + x2 = 468 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 = 468 + 9 Reorder the terms: 9 + -6x + x2 = 468 + 9 Combine like terms: 468 + 9 = 477 9 + -6x + x2 = 477 Factor a perfect square on the left side: (x + -3)(x + -3) = 477 Calculate the square root of the right side: 21.840329668 Break this problem into two subproblems by setting (x + -3) equal to 21.840329668 and -21.840329668.Subproblem 1
x + -3 = 21.840329668 Simplifying x + -3 = 21.840329668 Reorder the terms: -3 + x = 21.840329668 Solving -3 + x = 21.840329668 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 = 21.840329668 + 3 Combine like terms: -3 + 3 = 0 0 + x = 21.840329668 + 3 x = 21.840329668 + 3 Combine like terms: 21.840329668 + 3 = 24.840329668 x = 24.840329668 Simplifying x = 24.840329668Subproblem 2
x + -3 = -21.840329668 Simplifying x + -3 = -21.840329668 Reorder the terms: -3 + x = -21.840329668 Solving -3 + x = -21.840329668 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 = -21.840329668 + 3 Combine like terms: -3 + 3 = 0 0 + x = -21.840329668 + 3 x = -21.840329668 + 3 Combine like terms: -21.840329668 + 3 = -18.840329668 x = -18.840329668 Simplifying x = -18.840329668Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.840329668, -18.840329668}Solution
x = {24.840329668, -18.840329668}
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