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Simplifying 2x2 + -5x + -25 = x2 + 10x + 25 Reorder the terms: -25 + -5x + 2x2 = x2 + 10x + 25 Reorder the terms: -25 + -5x + 2x2 = 25 + 10x + x2 Solving -25 + -5x + 2x2 = 25 + 10x + x2 Solving for variable 'x'. Reorder the terms: -25 + -25 + -5x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: -25 + -25 = -50 -50 + -5x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: -5x + -10x = -15x -50 + -15x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -50 + -15x + 1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Reorder the terms: -50 + -15x + 1x2 = 25 + -25 + 10x + -10x + x2 + -1x2 Combine like terms: 25 + -25 = 0 -50 + -15x + 1x2 = 0 + 10x + -10x + x2 + -1x2 -50 + -15x + 1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -50 + -15x + 1x2 = 0 + x2 + -1x2 -50 + -15x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + -15x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -15x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -15x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -15x + x2 = 0 + 50 -15x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -15x + x2 = 50 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 50 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + -15x + x2 = 106.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -7.5 = 10.307764064 Simplifying x + -7.5 = 10.307764064 Reorder the terms: -7.5 + x = 10.307764064 Solving -7.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10.307764064 + 7.5 x = 10.307764064 + 7.5 Combine like terms: 10.307764064 + 7.5 = 17.807764064 x = 17.807764064 Simplifying x = 17.807764064Subproblem 2
x + -7.5 = -10.307764064 Simplifying x + -7.5 = -10.307764064 Reorder the terms: -7.5 + x = -10.307764064 Solving -7.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10.307764064 + 7.5 x = -10.307764064 + 7.5 Combine like terms: -10.307764064 + 7.5 = -2.807764064 x = -2.807764064 Simplifying x = -2.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.807764064, -2.807764064}
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