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Simplifying (16x2) + -40x = 23 Reorder the terms: -40x + (16x2) = 23 Solving -40x + (16x2) = 23 Solving for variable 'x'. Reorder the terms: -23 + -40x + (16x2) = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -40x + (16x2) = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.4375 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.4375' to each side of the equation. -1.4375 + -2.5x + 1.4375 + x2 = 0 + 1.4375 Reorder the terms: -1.4375 + 1.4375 + -2.5x + x2 = 0 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + -2.5x + x2 = 0 + 1.4375 -2.5x + x2 = 0 + 1.4375 Combine like terms: 0 + 1.4375 = 1.4375 -2.5x + x2 = 1.4375 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.4375 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.4375 + 1.5625 Combine like terms: 1.4375 + 1.5625 = 3 1.5625 + -2.5x + x2 = 3 Factor a perfect square on the left side: ((x) + -1.25)((x) + -1.25) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting ((x) + -1.25) equal to 1.732050808 and -1.732050808.Subproblem 1
(x) + -1.25 = 1.732050808 Simplifying (x) + -1.25 = 1.732050808 x + -1.25 = 1.732050808 Reorder the terms: -1.25 + x = 1.732050808 Solving -1.25 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.732050808 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.732050808 + 1.25 x = 1.732050808 + 1.25 Combine like terms: 1.732050808 + 1.25 = 2.982050808 x = 2.982050808 Simplifying x = 2.982050808Subproblem 2
(x) + -1.25 = -1.732050808 Simplifying (x) + -1.25 = -1.732050808 x + -1.25 = -1.732050808 Reorder the terms: -1.25 + x = -1.732050808 Solving -1.25 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.732050808 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.732050808 + 1.25 x = -1.732050808 + 1.25 Combine like terms: -1.732050808 + 1.25 = -0.482050808 x = -0.482050808 Simplifying x = -0.482050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.982050808, -0.482050808}
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