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Simplifying 0 = 0.1x2 + 27x + -1700 Reorder the terms: 0 = -1700 + 27x + 0.1x2 Solving 0 = -1700 + 27x + 0.1x2 Solving for variable 'x'. Combine like terms: 0 + 1700 = 1700 1700 + -27x + -0.1x2 = -1700 + 27x + 0.1x2 + 1700 + -27x + -0.1x2 Reorder the terms: 1700 + -27x + -0.1x2 = -1700 + 1700 + 27x + -27x + 0.1x2 + -0.1x2 Combine like terms: -1700 + 1700 = 0 1700 + -27x + -0.1x2 = 0 + 27x + -27x + 0.1x2 + -0.1x2 1700 + -27x + -0.1x2 = 27x + -27x + 0.1x2 + -0.1x2 Combine like terms: 27x + -27x = 0 1700 + -27x + -0.1x2 = 0 + 0.1x2 + -0.1x2 1700 + -27x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 1700 + -27x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -17000 + 270x + x2 = 0 Move the constant term to the right: Add '17000' to each side of the equation. -17000 + 270x + 17000 + x2 = 0 + 17000 Reorder the terms: -17000 + 17000 + 270x + x2 = 0 + 17000 Combine like terms: -17000 + 17000 = 0 0 + 270x + x2 = 0 + 17000 270x + x2 = 0 + 17000 Combine like terms: 0 + 17000 = 17000 270x + x2 = 17000 The x term is 270x. Take half its coefficient (135). Square it (18225) and add it to both sides. Add '18225' to each side of the equation. 270x + 18225 + x2 = 17000 + 18225 Reorder the terms: 18225 + 270x + x2 = 17000 + 18225 Combine like terms: 17000 + 18225 = 35225 18225 + 270x + x2 = 35225 Factor a perfect square on the left side: (x + 135)(x + 135) = 35225 Calculate the square root of the right side: 187.683243791 Break this problem into two subproblems by setting (x + 135) equal to 187.683243791 and -187.683243791.Subproblem 1
x + 135 = 187.683243791 Simplifying x + 135 = 187.683243791 Reorder the terms: 135 + x = 187.683243791 Solving 135 + x = 187.683243791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-135' to each side of the equation. 135 + -135 + x = 187.683243791 + -135 Combine like terms: 135 + -135 = 0 0 + x = 187.683243791 + -135 x = 187.683243791 + -135 Combine like terms: 187.683243791 + -135 = 52.683243791 x = 52.683243791 Simplifying x = 52.683243791Subproblem 2
x + 135 = -187.683243791 Simplifying x + 135 = -187.683243791 Reorder the terms: 135 + x = -187.683243791 Solving 135 + x = -187.683243791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-135' to each side of the equation. 135 + -135 + x = -187.683243791 + -135 Combine like terms: 135 + -135 = 0 0 + x = -187.683243791 + -135 x = -187.683243791 + -135 Combine like terms: -187.683243791 + -135 = -322.683243791 x = -322.683243791 Simplifying x = -322.683243791Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.683243791, -322.683243791}
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