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Simplifying 3x2 + -5 + -15x2 + 12 + 6x = 0 Reorder the terms: -5 + 12 + 6x + 3x2 + -15x2 = 0 Combine like terms: -5 + 12 = 7 7 + 6x + 3x2 + -15x2 = 0 Combine like terms: 3x2 + -15x2 = -12x2 7 + 6x + -12x2 = 0 Solving 7 + 6x + -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'. -0.5833333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -0.5x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -0.5x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.5833333333 -0.5x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -0.5x + x2 = 0.5833333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.5833333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.5833333333 + 0.0625 Combine like terms: 0.5833333333 + 0.0625 = 0.6458333333 0.0625 + -0.5x + x2 = 0.6458333333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.6458333333 Calculate the square root of the right side: 0.803637563 Break this problem into two subproblems by setting (x + -0.25) equal to 0.803637563 and -0.803637563.Subproblem 1
x + -0.25 = 0.803637563 Simplifying x + -0.25 = 0.803637563 Reorder the terms: -0.25 + x = 0.803637563 Solving -0.25 + x = 0.803637563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.803637563 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.803637563 + 0.25 x = 0.803637563 + 0.25 Combine like terms: 0.803637563 + 0.25 = 1.053637563 x = 1.053637563 Simplifying x = 1.053637563Subproblem 2
x + -0.25 = -0.803637563 Simplifying x + -0.25 = -0.803637563 Reorder the terms: -0.25 + x = -0.803637563 Solving -0.25 + x = -0.803637563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.803637563 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.803637563 + 0.25 x = -0.803637563 + 0.25 Combine like terms: -0.803637563 + 0.25 = -0.553637563 x = -0.553637563 Simplifying x = -0.553637563Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.053637563, -0.553637563}
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