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Simplifying 4x2 + -3 + -16 = -2x2 + -2x + -4 Reorder the terms: -3 + -16 + 4x2 = -2x2 + -2x + -4 Combine like terms: -3 + -16 = -19 -19 + 4x2 = -2x2 + -2x + -4 Reorder the terms: -19 + 4x2 = -4 + -2x + -2x2 Solving -19 + 4x2 = -4 + -2x + -2x2 Solving for variable 'x'. Reorder the terms: -19 + 4 + 2x + 4x2 + 2x2 = -4 + -2x + -2x2 + 4 + 2x + 2x2 Combine like terms: -19 + 4 = -15 -15 + 2x + 4x2 + 2x2 = -4 + -2x + -2x2 + 4 + 2x + 2x2 Combine like terms: 4x2 + 2x2 = 6x2 -15 + 2x + 6x2 = -4 + -2x + -2x2 + 4 + 2x + 2x2 Reorder the terms: -15 + 2x + 6x2 = -4 + 4 + -2x + 2x + -2x2 + 2x2 Combine like terms: -4 + 4 = 0 -15 + 2x + 6x2 = 0 + -2x + 2x + -2x2 + 2x2 -15 + 2x + 6x2 = -2x + 2x + -2x2 + 2x2 Combine like terms: -2x + 2x = 0 -15 + 2x + 6x2 = 0 + -2x2 + 2x2 -15 + 2x + 6x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -15 + 2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.3333333333x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.3333333333x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.3333333333x + x2 = 0 + 2.5 0.3333333333x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.3333333333x + x2 = 2.5 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 2.5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 2.5 + 0.02777777779 Combine like terms: 2.5 + 0.02777777779 = 2.52777777779 0.02777777779 + 0.3333333333x + x2 = 2.52777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 2.52777777779 Calculate the square root of the right side: 1.589898669 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.589898669 and -1.589898669.Subproblem 1
x + 0.1666666667 = 1.589898669 Simplifying x + 0.1666666667 = 1.589898669 Reorder the terms: 0.1666666667 + x = 1.589898669 Solving 0.1666666667 + x = 1.589898669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.589898669 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.589898669 + -0.1666666667 x = 1.589898669 + -0.1666666667 Combine like terms: 1.589898669 + -0.1666666667 = 1.4232320023 x = 1.4232320023 Simplifying x = 1.4232320023Subproblem 2
x + 0.1666666667 = -1.589898669 Simplifying x + 0.1666666667 = -1.589898669 Reorder the terms: 0.1666666667 + x = -1.589898669 Solving 0.1666666667 + x = -1.589898669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.589898669 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.589898669 + -0.1666666667 x = -1.589898669 + -0.1666666667 Combine like terms: -1.589898669 + -0.1666666667 = -1.7565653357 x = -1.7565653357 Simplifying x = -1.7565653357Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4232320023, -1.7565653357}
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