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Simplifying 152.41 + -250.52x + 96x2 = 0 Solving 152.41 + -250.52x + 96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. 1.587604167 + -2.609583333x + x2 = 0 Move the constant term to the right: Add '-1.587604167' to each side of the equation. 1.587604167 + -2.609583333x + -1.587604167 + x2 = 0 + -1.587604167 Reorder the terms: 1.587604167 + -1.587604167 + -2.609583333x + x2 = 0 + -1.587604167 Combine like terms: 1.587604167 + -1.587604167 = 0.000000000 0.000000000 + -2.609583333x + x2 = 0 + -1.587604167 -2.609583333x + x2 = 0 + -1.587604167 Combine like terms: 0 + -1.587604167 = -1.587604167 -2.609583333x + x2 = -1.587604167 The x term is -2.609583333x. Take half its coefficient (-1.304791667). Square it (1.702481294) and add it to both sides. Add '1.702481294' to each side of the equation. -2.609583333x + 1.702481294 + x2 = -1.587604167 + 1.702481294 Reorder the terms: 1.702481294 + -2.609583333x + x2 = -1.587604167 + 1.702481294 Combine like terms: -1.587604167 + 1.702481294 = 0.114877127 1.702481294 + -2.609583333x + x2 = 0.114877127 Factor a perfect square on the left side: (x + -1.304791667)(x + -1.304791667) = 0.114877127 Calculate the square root of the right side: 0.338935284 Break this problem into two subproblems by setting (x + -1.304791667) equal to 0.338935284 and -0.338935284.Subproblem 1
x + -1.304791667 = 0.338935284 Simplifying x + -1.304791667 = 0.338935284 Reorder the terms: -1.304791667 + x = 0.338935284 Solving -1.304791667 + x = 0.338935284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.304791667' to each side of the equation. -1.304791667 + 1.304791667 + x = 0.338935284 + 1.304791667 Combine like terms: -1.304791667 + 1.304791667 = 0.000000000 0.000000000 + x = 0.338935284 + 1.304791667 x = 0.338935284 + 1.304791667 Combine like terms: 0.338935284 + 1.304791667 = 1.643726951 x = 1.643726951 Simplifying x = 1.643726951Subproblem 2
x + -1.304791667 = -0.338935284 Simplifying x + -1.304791667 = -0.338935284 Reorder the terms: -1.304791667 + x = -0.338935284 Solving -1.304791667 + x = -0.338935284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.304791667' to each side of the equation. -1.304791667 + 1.304791667 + x = -0.338935284 + 1.304791667 Combine like terms: -1.304791667 + 1.304791667 = 0.000000000 0.000000000 + x = -0.338935284 + 1.304791667 x = -0.338935284 + 1.304791667 Combine like terms: -0.338935284 + 1.304791667 = 0.965856383 x = 0.965856383 Simplifying x = 0.965856383Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.643726951, 0.965856383}
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