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Simplifying 0 = x2 + -50x + -10000 Reorder the terms: 0 = -10000 + -50x + x2 Solving 0 = -10000 + -50x + x2 Solving for variable 'x'. Combine like terms: 0 + 10000 = 10000 10000 + 50x + -1x2 = -10000 + -50x + x2 + 10000 + 50x + -1x2 Reorder the terms: 10000 + 50x + -1x2 = -10000 + 10000 + -50x + 50x + x2 + -1x2 Combine like terms: -10000 + 10000 = 0 10000 + 50x + -1x2 = 0 + -50x + 50x + x2 + -1x2 10000 + 50x + -1x2 = -50x + 50x + x2 + -1x2 Combine like terms: -50x + 50x = 0 10000 + 50x + -1x2 = 0 + x2 + -1x2 10000 + 50x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10000 + 50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10000 + -50x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + -50x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + -50x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + -50x + x2 = 0 + 10000 -50x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 -50x + x2 = 10000 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 10000 + 625 Reorder the terms: 625 + -50x + x2 = 10000 + 625 Combine like terms: 10000 + 625 = 10625 625 + -50x + x2 = 10625 Factor a perfect square on the left side: (x + -25)(x + -25) = 10625 Calculate the square root of the right side: 103.07764064 Break this problem into two subproblems by setting (x + -25) equal to 103.07764064 and -103.07764064.Subproblem 1
x + -25 = 103.07764064 Simplifying x + -25 = 103.07764064 Reorder the terms: -25 + x = 103.07764064 Solving -25 + x = 103.07764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 103.07764064 + 25 Combine like terms: -25 + 25 = 0 0 + x = 103.07764064 + 25 x = 103.07764064 + 25 Combine like terms: 103.07764064 + 25 = 128.07764064 x = 128.07764064 Simplifying x = 128.07764064Subproblem 2
x + -25 = -103.07764064 Simplifying x + -25 = -103.07764064 Reorder the terms: -25 + x = -103.07764064 Solving -25 + x = -103.07764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -103.07764064 + 25 Combine like terms: -25 + 25 = 0 0 + x = -103.07764064 + 25 x = -103.07764064 + 25 Combine like terms: -103.07764064 + 25 = -78.07764064 x = -78.07764064 Simplifying x = -78.07764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.07764064, -78.07764064}
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