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Simplifying 25x2 + 20x = 6 Reorder the terms: 20x + 25x2 = 6 Solving 20x + 25x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 20x + 25x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.24 + 0.8x + x2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + 0.8x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + 0.8x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + 0.8x + x2 = 0 + 0.24 0.8x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 0.8x + x2 = 0.24 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 = 0.24 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.24 + 0.16 Combine like terms: 0.24 + 0.16 = 0.4 0.16 + 0.8x + x2 = 0.4 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + 0.4) equal to 0.632455532 and -0.632455532.Subproblem 1
x + 0.4 = 0.632455532 Simplifying x + 0.4 = 0.632455532 Reorder the terms: 0.4 + x = 0.632455532 Solving 0.4 + x = 0.632455532 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 = 0.632455532 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.632455532 + -0.4 x = 0.632455532 + -0.4 Combine like terms: 0.632455532 + -0.4 = 0.232455532 x = 0.232455532 Simplifying x = 0.232455532Subproblem 2
x + 0.4 = -0.632455532 Simplifying x + 0.4 = -0.632455532 Reorder the terms: 0.4 + x = -0.632455532 Solving 0.4 + x = -0.632455532 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 = -0.632455532 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.632455532 + -0.4 x = -0.632455532 + -0.4 Combine like terms: -0.632455532 + -0.4 = -1.032455532 x = -1.032455532 Simplifying x = -1.032455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.232455532, -1.032455532}
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