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Simplifying x2 + 25x = 0.97 Reorder the terms: 25x + x2 = 0.97 Solving 25x + x2 = 0.97 Solving for variable 'x'. Reorder the terms: -0.97 + 25x + x2 = 0.97 + -0.97 Combine like terms: 0.97 + -0.97 = 0.00 -0.97 + 25x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.97' to each side of the equation. -0.97 + 25x + 0.97 + x2 = 0.00 + 0.97 Reorder the terms: -0.97 + 0.97 + 25x + x2 = 0.00 + 0.97 Combine like terms: -0.97 + 0.97 = 0.00 0.00 + 25x + x2 = 0.00 + 0.97 25x + x2 = 0.00 + 0.97 Combine like terms: 0.00 + 0.97 = 0.97 25x + x2 = 0.97 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 0.97 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 0.97 + 156.25 Combine like terms: 0.97 + 156.25 = 157.22 156.25 + 25x + x2 = 157.22 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 157.22 Calculate the square root of the right side: 12.538739969 Break this problem into two subproblems by setting (x + 12.5) equal to 12.538739969 and -12.538739969.Subproblem 1
x + 12.5 = 12.538739969 Simplifying x + 12.5 = 12.538739969 Reorder the terms: 12.5 + x = 12.538739969 Solving 12.5 + x = 12.538739969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.538739969 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.538739969 + -12.5 x = 12.538739969 + -12.5 Combine like terms: 12.538739969 + -12.5 = 0.038739969 x = 0.038739969 Simplifying x = 0.038739969Subproblem 2
x + 12.5 = -12.538739969 Simplifying x + 12.5 = -12.538739969 Reorder the terms: 12.5 + x = -12.538739969 Solving 12.5 + x = -12.538739969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.538739969 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.538739969 + -12.5 x = -12.538739969 + -12.5 Combine like terms: -12.538739969 + -12.5 = -25.038739969 x = -25.038739969 Simplifying x = -25.038739969Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.038739969, -25.038739969}
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