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Simplifying 1.5 = -0.0001x2 + 0.0304x + 1.1696 Reorder the terms: 1.5 = 1.1696 + 0.0304x + -0.0001x2 Solving 1.5 = 1.1696 + 0.0304x + -0.0001x2 Solving for variable 'x'. Combine like terms: 1.5 + -1.1696 = 0.3304 0.3304 + -0.0304x + 0.0001x2 = 1.1696 + 0.0304x + -0.0001x2 + -1.1696 + -0.0304x + 0.0001x2 Reorder the terms: 0.3304 + -0.0304x + 0.0001x2 = 1.1696 + -1.1696 + 0.0304x + -0.0304x + -0.0001x2 + 0.0001x2 Combine like terms: 1.1696 + -1.1696 = 0.0000 0.3304 + -0.0304x + 0.0001x2 = 0.0000 + 0.0304x + -0.0304x + -0.0001x2 + 0.0001x2 0.3304 + -0.0304x + 0.0001x2 = 0.0304x + -0.0304x + -0.0001x2 + 0.0001x2 Combine like terms: 0.0304x + -0.0304x = 0.0000 0.3304 + -0.0304x + 0.0001x2 = 0.0000 + -0.0001x2 + 0.0001x2 0.3304 + -0.0304x + 0.0001x2 = -0.0001x2 + 0.0001x2 Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000 0.3304 + -0.0304x + 0.0001x2 = 0.0000 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. 3304 + -304x + x2 = 0 Move the constant term to the right: Add '-3304' to each side of the equation. 3304 + -304x + -3304 + x2 = 0 + -3304 Reorder the terms: 3304 + -3304 + -304x + x2 = 0 + -3304 Combine like terms: 3304 + -3304 = 0 0 + -304x + x2 = 0 + -3304 -304x + x2 = 0 + -3304 Combine like terms: 0 + -3304 = -3304 -304x + x2 = -3304 The x term is -304x. Take half its coefficient (-152). Square it (23104) and add it to both sides. Add '23104' to each side of the equation. -304x + 23104 + x2 = -3304 + 23104 Reorder the terms: 23104 + -304x + x2 = -3304 + 23104 Combine like terms: -3304 + 23104 = 19800 23104 + -304x + x2 = 19800 Factor a perfect square on the left side: (x + -152)(x + -152) = 19800 Calculate the square root of the right side: 140.712472795 Break this problem into two subproblems by setting (x + -152) equal to 140.712472795 and -140.712472795.Subproblem 1
x + -152 = 140.712472795 Simplifying x + -152 = 140.712472795 Reorder the terms: -152 + x = 140.712472795 Solving -152 + x = 140.712472795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '152' to each side of the equation. -152 + 152 + x = 140.712472795 + 152 Combine like terms: -152 + 152 = 0 0 + x = 140.712472795 + 152 x = 140.712472795 + 152 Combine like terms: 140.712472795 + 152 = 292.712472795 x = 292.712472795 Simplifying x = 292.712472795Subproblem 2
x + -152 = -140.712472795 Simplifying x + -152 = -140.712472795 Reorder the terms: -152 + x = -140.712472795 Solving -152 + x = -140.712472795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '152' to each side of the equation. -152 + 152 + x = -140.712472795 + 152 Combine like terms: -152 + 152 = 0 0 + x = -140.712472795 + 152 x = -140.712472795 + 152 Combine like terms: -140.712472795 + 152 = 11.287527205 x = 11.287527205 Simplifying x = 11.287527205Solution
The solution to the problem is based on the solutions from the subproblems. x = {292.712472795, 11.287527205}
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