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Simplifying 3x2 + 12x + -54 = 2 Reorder the terms: -54 + 12x + 3x2 = 2 Solving -54 + 12x + 3x2 = 2 Solving for variable 'x'. Reorder the terms: -54 + -2 + 12x + 3x2 = 2 + -2 Combine like terms: -54 + -2 = -56 -56 + 12x + 3x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -56 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18.66666667 + 4x + x2 = 0 Move the constant term to the right: Add '18.66666667' to each side of the equation. -18.66666667 + 4x + 18.66666667 + x2 = 0 + 18.66666667 Reorder the terms: -18.66666667 + 18.66666667 + 4x + x2 = 0 + 18.66666667 Combine like terms: -18.66666667 + 18.66666667 = 0.00000000 0.00000000 + 4x + x2 = 0 + 18.66666667 4x + x2 = 0 + 18.66666667 Combine like terms: 0 + 18.66666667 = 18.66666667 4x + x2 = 18.66666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 18.66666667 + 4 Reorder the terms: 4 + 4x + x2 = 18.66666667 + 4 Combine like terms: 18.66666667 + 4 = 22.66666667 4 + 4x + x2 = 22.66666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 22.66666667 Calculate the square root of the right side: 4.760952286 Break this problem into two subproblems by setting (x + 2) equal to 4.760952286 and -4.760952286.Subproblem 1
x + 2 = 4.760952286 Simplifying x + 2 = 4.760952286 Reorder the terms: 2 + x = 4.760952286 Solving 2 + x = 4.760952286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.760952286 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.760952286 + -2 x = 4.760952286 + -2 Combine like terms: 4.760952286 + -2 = 2.760952286 x = 2.760952286 Simplifying x = 2.760952286Subproblem 2
x + 2 = -4.760952286 Simplifying x + 2 = -4.760952286 Reorder the terms: 2 + x = -4.760952286 Solving 2 + x = -4.760952286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.760952286 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.760952286 + -2 x = -4.760952286 + -2 Combine like terms: -4.760952286 + -2 = -6.760952286 x = -6.760952286 Simplifying x = -6.760952286Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.760952286, -6.760952286}
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