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Simplifying 0 = x2 + -25x + -11 Reorder the terms: 0 = -11 + -25x + x2 Solving 0 = -11 + -25x + x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + 25x + -1x2 = -11 + -25x + x2 + 11 + 25x + -1x2 Reorder the terms: 11 + 25x + -1x2 = -11 + 11 + -25x + 25x + x2 + -1x2 Combine like terms: -11 + 11 = 0 11 + 25x + -1x2 = 0 + -25x + 25x + x2 + -1x2 11 + 25x + -1x2 = -25x + 25x + x2 + -1x2 Combine like terms: -25x + 25x = 0 11 + 25x + -1x2 = 0 + x2 + -1x2 11 + 25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -25x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -25x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -25x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -25x + x2 = 0 + 11 -25x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -25x + x2 = 11 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 = 11 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 11 + 156.25 Combine like terms: 11 + 156.25 = 167.25 156.25 + -25x + x2 = 167.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 167.25 Calculate the square root of the right side: 12.932517156 Break this problem into two subproblems by setting (x + -12.5) equal to 12.932517156 and -12.932517156.Subproblem 1
x + -12.5 = 12.932517156 Simplifying x + -12.5 = 12.932517156 Reorder the terms: -12.5 + x = 12.932517156 Solving -12.5 + x = 12.932517156 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 = 12.932517156 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.932517156 + 12.5 x = 12.932517156 + 12.5 Combine like terms: 12.932517156 + 12.5 = 25.432517156 x = 25.432517156 Simplifying x = 25.432517156Subproblem 2
x + -12.5 = -12.932517156 Simplifying x + -12.5 = -12.932517156 Reorder the terms: -12.5 + x = -12.932517156 Solving -12.5 + x = -12.932517156 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 = -12.932517156 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.932517156 + 12.5 x = -12.932517156 + 12.5 Combine like terms: -12.932517156 + 12.5 = -0.432517156 x = -0.432517156 Simplifying x = -0.432517156Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.432517156, -0.432517156}
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