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Simplifying 25x2 + 34x = 45 Reorder the terms: 34x + 25x2 = 45 Solving 34x + 25x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 34x + 25x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 34x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.8 + 1.36x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 1.36x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 1.36x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 1.36x + x2 = 0 + 1.8 1.36x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 1.36x + x2 = 1.8 The x term is 1.36x. Take half its coefficient (0.68). Square it (0.4624) and add it to both sides. Add '0.4624' to each side of the equation. 1.36x + 0.4624 + x2 = 1.8 + 0.4624 Reorder the terms: 0.4624 + 1.36x + x2 = 1.8 + 0.4624 Combine like terms: 1.8 + 0.4624 = 2.2624 0.4624 + 1.36x + x2 = 2.2624 Factor a perfect square on the left side: (x + 0.68)(x + 0.68) = 2.2624 Calculate the square root of the right side: 1.504127654 Break this problem into two subproblems by setting (x + 0.68) equal to 1.504127654 and -1.504127654.Subproblem 1
x + 0.68 = 1.504127654 Simplifying x + 0.68 = 1.504127654 Reorder the terms: 0.68 + x = 1.504127654 Solving 0.68 + x = 1.504127654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.68' to each side of the equation. 0.68 + -0.68 + x = 1.504127654 + -0.68 Combine like terms: 0.68 + -0.68 = 0.00 0.00 + x = 1.504127654 + -0.68 x = 1.504127654 + -0.68 Combine like terms: 1.504127654 + -0.68 = 0.824127654 x = 0.824127654 Simplifying x = 0.824127654Subproblem 2
x + 0.68 = -1.504127654 Simplifying x + 0.68 = -1.504127654 Reorder the terms: 0.68 + x = -1.504127654 Solving 0.68 + x = -1.504127654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.68' to each side of the equation. 0.68 + -0.68 + x = -1.504127654 + -0.68 Combine like terms: 0.68 + -0.68 = 0.00 0.00 + x = -1.504127654 + -0.68 x = -1.504127654 + -0.68 Combine like terms: -1.504127654 + -0.68 = -2.184127654 x = -2.184127654 Simplifying x = -2.184127654Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.824127654, -2.184127654}
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