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Simplifying 25x + -10 = x2 Reorder the terms: -10 + 25x = x2 Solving -10 + 25x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -10 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -25x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -25x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -25x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -25x + x2 = 0 + -10 -25x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -25x + x2 = -10 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 = -10 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -10 + 156.25 Combine like terms: -10 + 156.25 = 146.25 156.25 + -25x + x2 = 146.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + -12.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + -12.5 = 12.093386622 Simplifying x + -12.5 = 12.093386622 Reorder the terms: -12.5 + x = 12.093386622 Solving -12.5 + x = 12.093386622 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 = 12.093386622 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.093386622 + 12.5 x = 12.093386622 + 12.5 Combine like terms: 12.093386622 + 12.5 = 24.593386622 x = 24.593386622 Simplifying x = 24.593386622Subproblem 2
x + -12.5 = -12.093386622 Simplifying x + -12.5 = -12.093386622 Reorder the terms: -12.5 + x = -12.093386622 Solving -12.5 + x = -12.093386622 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 = -12.093386622 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.093386622 + 12.5 x = -12.093386622 + 12.5 Combine like terms: -12.093386622 + 12.5 = 0.406613378 x = 0.406613378 Simplifying x = 0.406613378Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.593386622, 0.406613378}
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