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Simplifying 8x + -3 + -12x2 + -12x + 18 = 0 Reorder the terms: -3 + 18 + 8x + -12x + -12x2 = 0 Combine like terms: -3 + 18 = 15 15 + 8x + -12x + -12x2 = 0 Combine like terms: 8x + -12x = -4x 15 + -4x + -12x2 = 0 Solving 15 + -4x + -12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.25 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.3333333333x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.3333333333x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.3333333333x + x2 = 0 + 1.25 0.3333333333x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.3333333333x + x2 = 1.25 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 = 1.25 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 1.25 + 0.02777777779 Combine like terms: 1.25 + 0.02777777779 = 1.27777777779 0.02777777779 + 0.3333333333x + x2 = 1.27777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 1.27777777779 Calculate the square root of the right side: 1.130388331 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.130388331 and -1.130388331.Subproblem 1
x + 0.1666666667 = 1.130388331 Simplifying x + 0.1666666667 = 1.130388331 Reorder the terms: 0.1666666667 + x = 1.130388331 Solving 0.1666666667 + x = 1.130388331 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 = 1.130388331 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.130388331 + -0.1666666667 x = 1.130388331 + -0.1666666667 Combine like terms: 1.130388331 + -0.1666666667 = 0.9637216643 x = 0.9637216643 Simplifying x = 0.9637216643Subproblem 2
x + 0.1666666667 = -1.130388331 Simplifying x + 0.1666666667 = -1.130388331 Reorder the terms: 0.1666666667 + x = -1.130388331 Solving 0.1666666667 + x = -1.130388331 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 = -1.130388331 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.130388331 + -0.1666666667 x = -1.130388331 + -0.1666666667 Combine like terms: -1.130388331 + -0.1666666667 = -1.2970549977 x = -1.2970549977 Simplifying x = -1.2970549977Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9637216643, -1.2970549977}
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