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Simplifying 0.1x2 + 0.6x + -12 = 0 Reorder the terms: -12 + 0.6x + 0.1x2 = 0 Solving -12 + 0.6x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -120 + 6x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 6x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 6x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 6x + x2 = 0 + 120 6x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 6x + x2 = 120 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 120 + 9 Reorder the terms: 9 + 6x + x2 = 120 + 9 Combine like terms: 120 + 9 = 129 9 + 6x + x2 = 129 Factor a perfect square on the left side: (x + 3)(x + 3) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 3) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 3 = 11.357816692 Simplifying x + 3 = 11.357816692 Reorder the terms: 3 + x = 11.357816692 Solving 3 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 11.357816692 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.357816692 + -3 x = 11.357816692 + -3 Combine like terms: 11.357816692 + -3 = 8.357816692 x = 8.357816692 Simplifying x = 8.357816692Subproblem 2
x + 3 = -11.357816692 Simplifying x + 3 = -11.357816692 Reorder the terms: 3 + x = -11.357816692 Solving 3 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -11.357816692 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.357816692 + -3 x = -11.357816692 + -3 Combine like terms: -11.357816692 + -3 = -14.357816692 x = -14.357816692 Simplifying x = -14.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.357816692, -14.357816692}
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