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Simplifying 49x = 100 + x2 Solving 49x = 100 + x2 Solving for variable 'x'. Reorder the terms: -100 + 49x + -1x2 = 100 + x2 + -100 + -1x2 Reorder the terms: -100 + 49x + -1x2 = 100 + -100 + x2 + -1x2 Combine like terms: 100 + -100 = 0 -100 + 49x + -1x2 = 0 + x2 + -1x2 -100 + 49x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -100 + 49x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -49x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -49x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -49x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -49x + x2 = 0 + -100 -49x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -49x + x2 = -100 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = -100 + 600.25 Reorder the terms: 600.25 + -49x + x2 = -100 + 600.25 Combine like terms: -100 + 600.25 = 500.25 600.25 + -49x + x2 = 500.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 500.25 Calculate the square root of the right side: 22.366269246 Break this problem into two subproblems by setting (x + -24.5) equal to 22.366269246 and -22.366269246.Subproblem 1
x + -24.5 = 22.366269246 Simplifying x + -24.5 = 22.366269246 Reorder the terms: -24.5 + x = 22.366269246 Solving -24.5 + x = 22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 22.366269246 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 22.366269246 + 24.5 x = 22.366269246 + 24.5 Combine like terms: 22.366269246 + 24.5 = 46.866269246 x = 46.866269246 Simplifying x = 46.866269246Subproblem 2
x + -24.5 = -22.366269246 Simplifying x + -24.5 = -22.366269246 Reorder the terms: -24.5 + x = -22.366269246 Solving -24.5 + x = -22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -22.366269246 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -22.366269246 + 24.5 x = -22.366269246 + 24.5 Combine like terms: -22.366269246 + 24.5 = 2.133730754 x = 2.133730754 Simplifying x = 2.133730754Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.866269246, 2.133730754}
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