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Simplifying 0.5x2 + 6x + -2 = 0 Reorder the terms: -2 + 6x + 0.5x2 = 0 Solving -2 + 6x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -4 + 12x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 12x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 12x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 12x + x2 = 0 + 4 12x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 12x + x2 = 4 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 4 + 36 Reorder the terms: 36 + 12x + x2 = 4 + 36 Combine like terms: 4 + 36 = 40 36 + 12x + x2 = 40 Factor a perfect square on the left side: (x + 6)(x + 6) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 6) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 6 = 6.32455532 Simplifying x + 6 = 6.32455532 Reorder the terms: 6 + x = 6.32455532 Solving 6 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.32455532 + -6 x = 6.32455532 + -6 Combine like terms: 6.32455532 + -6 = 0.32455532 x = 0.32455532 Simplifying x = 0.32455532Subproblem 2
x + 6 = -6.32455532 Simplifying x + 6 = -6.32455532 Reorder the terms: 6 + x = -6.32455532 Solving 6 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.32455532 + -6 x = -6.32455532 + -6 Combine like terms: -6.32455532 + -6 = -12.32455532 x = -12.32455532 Simplifying x = -12.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.32455532, -12.32455532}
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