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Simplifying -1x2 + 12x + 252 = 0 Reorder the terms: 252 + 12x + -1x2 = 0 Solving 252 + 12x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -252 + -12x + x2 = 0 Move the constant term to the right: Add '252' to each side of the equation. -252 + -12x + 252 + x2 = 0 + 252 Reorder the terms: -252 + 252 + -12x + x2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + -12x + x2 = 0 + 252 -12x + x2 = 0 + 252 Combine like terms: 0 + 252 = 252 -12x + x2 = 252 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 252 + 36 Reorder the terms: 36 + -12x + x2 = 252 + 36 Combine like terms: 252 + 36 = 288 36 + -12x + x2 = 288 Factor a perfect square on the left side: (x + -6)(x + -6) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + -6) equal to 16.970562748 and -16.970562748.Subproblem 1
x + -6 = 16.970562748 Simplifying x + -6 = 16.970562748 Reorder the terms: -6 + x = 16.970562748 Solving -6 + x = 16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 16.970562748 + 6 Combine like terms: -6 + 6 = 0 0 + x = 16.970562748 + 6 x = 16.970562748 + 6 Combine like terms: 16.970562748 + 6 = 22.970562748 x = 22.970562748 Simplifying x = 22.970562748Subproblem 2
x + -6 = -16.970562748 Simplifying x + -6 = -16.970562748 Reorder the terms: -6 + x = -16.970562748 Solving -6 + x = -16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -16.970562748 + 6 Combine like terms: -6 + 6 = 0 0 + x = -16.970562748 + 6 x = -16.970562748 + 6 Combine like terms: -16.970562748 + 6 = -10.970562748 x = -10.970562748 Simplifying x = -10.970562748Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.970562748, -10.970562748}
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