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Simplifying 236 + -15x + -2x2 = 0 Solving 236 + -15x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -118 + 7.5x + x2 = 0 Move the constant term to the right: Add '118' to each side of the equation. -118 + 7.5x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 7.5x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 7.5x + x2 = 0 + 118 7.5x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 7.5x + x2 = 118 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 118 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 118 + 14.0625 Combine like terms: 118 + 14.0625 = 132.0625 14.0625 + 7.5x + x2 = 132.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 132.0625 Calculate the square root of the right side: 11.491844935 Break this problem into two subproblems by setting (x + 3.75) equal to 11.491844935 and -11.491844935.Subproblem 1
x + 3.75 = 11.491844935 Simplifying x + 3.75 = 11.491844935 Reorder the terms: 3.75 + x = 11.491844935 Solving 3.75 + x = 11.491844935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 11.491844935 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 11.491844935 + -3.75 x = 11.491844935 + -3.75 Combine like terms: 11.491844935 + -3.75 = 7.741844935 x = 7.741844935 Simplifying x = 7.741844935Subproblem 2
x + 3.75 = -11.491844935 Simplifying x + 3.75 = -11.491844935 Reorder the terms: 3.75 + x = -11.491844935 Solving 3.75 + x = -11.491844935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -11.491844935 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -11.491844935 + -3.75 x = -11.491844935 + -3.75 Combine like terms: -11.491844935 + -3.75 = -15.241844935 x = -15.241844935 Simplifying x = -15.241844935Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.741844935, -15.241844935}
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