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Simplifying x2 = 25x + -89 Reorder the terms: x2 = -89 + 25x Solving x2 = -89 + 25x Solving for variable 'x'. Reorder the terms: 89 + -25x + x2 = -89 + 25x + 89 + -25x Reorder the terms: 89 + -25x + x2 = -89 + 89 + 25x + -25x Combine like terms: -89 + 89 = 0 89 + -25x + x2 = 0 + 25x + -25x 89 + -25x + x2 = 25x + -25x Combine like terms: 25x + -25x = 0 89 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-89' to each side of the equation. 89 + -25x + -89 + x2 = 0 + -89 Reorder the terms: 89 + -89 + -25x + x2 = 0 + -89 Combine like terms: 89 + -89 = 0 0 + -25x + x2 = 0 + -89 -25x + x2 = 0 + -89 Combine like terms: 0 + -89 = -89 -25x + x2 = -89 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 = -89 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -89 + 156.25 Combine like terms: -89 + 156.25 = 67.25 156.25 + -25x + x2 = 67.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + -12.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + -12.5 = 8.200609733 Simplifying x + -12.5 = 8.200609733 Reorder the terms: -12.5 + x = 8.200609733 Solving -12.5 + x = 8.200609733 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 = 8.200609733 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 8.200609733 + 12.5 x = 8.200609733 + 12.5 Combine like terms: 8.200609733 + 12.5 = 20.700609733 x = 20.700609733 Simplifying x = 20.700609733Subproblem 2
x + -12.5 = -8.200609733 Simplifying x + -12.5 = -8.200609733 Reorder the terms: -12.5 + x = -8.200609733 Solving -12.5 + x = -8.200609733 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 = -8.200609733 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -8.200609733 + 12.5 x = -8.200609733 + 12.5 Combine like terms: -8.200609733 + 12.5 = 4.299390267 x = 4.299390267 Simplifying x = 4.299390267Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.700609733, 4.299390267}
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