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Simplifying 6 = 0.5x2 + 6x + -9 Reorder the terms: 6 = -9 + 6x + 0.5x2 Solving 6 = -9 + 6x + 0.5x2 Solving for variable 'x'. Combine like terms: 6 + 9 = 15 15 + -6x + -0.5x2 = -9 + 6x + 0.5x2 + 9 + -6x + -0.5x2 Reorder the terms: 15 + -6x + -0.5x2 = -9 + 9 + 6x + -6x + 0.5x2 + -0.5x2 Combine like terms: -9 + 9 = 0 15 + -6x + -0.5x2 = 0 + 6x + -6x + 0.5x2 + -0.5x2 15 + -6x + -0.5x2 = 6x + -6x + 0.5x2 + -0.5x2 Combine like terms: 6x + -6x = 0 15 + -6x + -0.5x2 = 0 + 0.5x2 + -0.5x2 15 + -6x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 15 + -6x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -30 + 12x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 12x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 12x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 12x + x2 = 0 + 30 12x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 12x + x2 = 30 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 = 30 + 36 Reorder the terms: 36 + 12x + x2 = 30 + 36 Combine like terms: 30 + 36 = 66 36 + 12x + x2 = 66 Factor a perfect square on the left side: (x + 6)(x + 6) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 6) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 6 = 8.124038405 Simplifying x + 6 = 8.124038405 Reorder the terms: 6 + x = 8.124038405 Solving 6 + x = 8.124038405 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 = 8.124038405 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.124038405 + -6 x = 8.124038405 + -6 Combine like terms: 8.124038405 + -6 = 2.124038405 x = 2.124038405 Simplifying x = 2.124038405Subproblem 2
x + 6 = -8.124038405 Simplifying x + 6 = -8.124038405 Reorder the terms: 6 + x = -8.124038405 Solving 6 + x = -8.124038405 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 = -8.124038405 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.124038405 + -6 x = -8.124038405 + -6 Combine like terms: -8.124038405 + -6 = -14.124038405 x = -14.124038405 Simplifying x = -14.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.124038405, -14.124038405}
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