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Simplifying 25x2 + -20x = 46 Reorder the terms: -20x + 25x2 = 46 Solving -20x + 25x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + -20x + 25x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.84 + -0.8x + x2 = 0 Move the constant term to the right: Add '1.84' to each side of the equation. -1.84 + -0.8x + 1.84 + x2 = 0 + 1.84 Reorder the terms: -1.84 + 1.84 + -0.8x + x2 = 0 + 1.84 Combine like terms: -1.84 + 1.84 = 0.00 0.00 + -0.8x + x2 = 0 + 1.84 -0.8x + x2 = 0 + 1.84 Combine like terms: 0 + 1.84 = 1.84 -0.8x + x2 = 1.84 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 1.84 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.84 + 0.16 Combine like terms: 1.84 + 0.16 = 2 0.16 + -0.8x + x2 = 2 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -0.4) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -0.4 = 1.414213562 Simplifying x + -0.4 = 1.414213562 Reorder the terms: -0.4 + x = 1.414213562 Solving -0.4 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.414213562 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.414213562 + 0.4 x = 1.414213562 + 0.4 Combine like terms: 1.414213562 + 0.4 = 1.814213562 x = 1.814213562 Simplifying x = 1.814213562Subproblem 2
x + -0.4 = -1.414213562 Simplifying x + -0.4 = -1.414213562 Reorder the terms: -0.4 + x = -1.414213562 Solving -0.4 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.414213562 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.414213562 + 0.4 x = -1.414213562 + 0.4 Combine like terms: -1.414213562 + 0.4 = -1.014213562 x = -1.014213562 Simplifying x = -1.014213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.814213562, -1.014213562}
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