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Simplifying 25x2 + 13x = 54 Reorder the terms: 13x + 25x2 = 54 Solving 13x + 25x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 13x + 25x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 13x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.16 + 0.52x + x2 = 0 Move the constant term to the right: Add '2.16' to each side of the equation. -2.16 + 0.52x + 2.16 + x2 = 0 + 2.16 Reorder the terms: -2.16 + 2.16 + 0.52x + x2 = 0 + 2.16 Combine like terms: -2.16 + 2.16 = 0.00 0.00 + 0.52x + x2 = 0 + 2.16 0.52x + x2 = 0 + 2.16 Combine like terms: 0 + 2.16 = 2.16 0.52x + x2 = 2.16 The x term is 0.52x. Take half its coefficient (0.26). Square it (0.0676) and add it to both sides. Add '0.0676' to each side of the equation. 0.52x + 0.0676 + x2 = 2.16 + 0.0676 Reorder the terms: 0.0676 + 0.52x + x2 = 2.16 + 0.0676 Combine like terms: 2.16 + 0.0676 = 2.2276 0.0676 + 0.52x + x2 = 2.2276 Factor a perfect square on the left side: (x + 0.26)(x + 0.26) = 2.2276 Calculate the square root of the right side: 1.492514657 Break this problem into two subproblems by setting (x + 0.26) equal to 1.492514657 and -1.492514657.Subproblem 1
x + 0.26 = 1.492514657 Simplifying x + 0.26 = 1.492514657 Reorder the terms: 0.26 + x = 1.492514657 Solving 0.26 + x = 1.492514657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.26' to each side of the equation. 0.26 + -0.26 + x = 1.492514657 + -0.26 Combine like terms: 0.26 + -0.26 = 0.00 0.00 + x = 1.492514657 + -0.26 x = 1.492514657 + -0.26 Combine like terms: 1.492514657 + -0.26 = 1.232514657 x = 1.232514657 Simplifying x = 1.232514657Subproblem 2
x + 0.26 = -1.492514657 Simplifying x + 0.26 = -1.492514657 Reorder the terms: 0.26 + x = -1.492514657 Solving 0.26 + x = -1.492514657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.26' to each side of the equation. 0.26 + -0.26 + x = -1.492514657 + -0.26 Combine like terms: 0.26 + -0.26 = 0.00 0.00 + x = -1.492514657 + -0.26 x = -1.492514657 + -0.26 Combine like terms: -1.492514657 + -0.26 = -1.752514657 x = -1.752514657 Simplifying x = -1.752514657Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.232514657, -1.752514657}
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