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Simplifying 25x2 + 20x = 7 Reorder the terms: 20x + 25x2 = 7 Solving 20x + 25x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 20x + 25x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.28 + 0.8x + x2 = 0 Move the constant term to the right: Add '0.28' to each side of the equation. -0.28 + 0.8x + 0.28 + x2 = 0 + 0.28 Reorder the terms: -0.28 + 0.28 + 0.8x + x2 = 0 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + 0.8x + x2 = 0 + 0.28 0.8x + x2 = 0 + 0.28 Combine like terms: 0 + 0.28 = 0.28 0.8x + x2 = 0.28 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 = 0.28 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.28 + 0.16 Combine like terms: 0.28 + 0.16 = 0.44 0.16 + 0.8x + x2 = 0.44 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + 0.4) equal to 0.663324958 and -0.663324958.Subproblem 1
x + 0.4 = 0.663324958 Simplifying x + 0.4 = 0.663324958 Reorder the terms: 0.4 + x = 0.663324958 Solving 0.4 + x = 0.663324958 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 = 0.663324958 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.663324958 + -0.4 x = 0.663324958 + -0.4 Combine like terms: 0.663324958 + -0.4 = 0.263324958 x = 0.263324958 Simplifying x = 0.263324958Subproblem 2
x + 0.4 = -0.663324958 Simplifying x + 0.4 = -0.663324958 Reorder the terms: 0.4 + x = -0.663324958 Solving 0.4 + x = -0.663324958 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 = -0.663324958 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.663324958 + -0.4 x = -0.663324958 + -0.4 Combine like terms: -0.663324958 + -0.4 = -1.063324958 x = -1.063324958 Simplifying x = -1.063324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.263324958, -1.063324958}
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