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Simplifying 3x2 + -12x + -46 = 10 Reorder the terms: -46 + -12x + 3x2 = 10 Solving -46 + -12x + 3x2 = 10 Solving for variable 'x'. Reorder the terms: -46 + -10 + -12x + 3x2 = 10 + -10 Combine like terms: -46 + -10 = -56 -56 + -12x + 3x2 = 10 + -10 Combine like terms: 10 + -10 = 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 = 6.760952286 x = 6.760952286 Simplifying x = 6.760952286Subproblem 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 = -2.760952286 x = -2.760952286 Simplifying x = -2.760952286Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.760952286, -2.760952286}
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