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Simplifying x = x2 + -14x + 49 Reorder the terms: x = 49 + -14x + x2 Solving x = 49 + -14x + x2 Solving for variable 'x'. Reorder the terms: -49 + x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Combine like terms: x + 14x = 15x -49 + 15x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2 Reorder the terms: -49 + 15x + -1x2 = 49 + -49 + -14x + 14x + x2 + -1x2 Combine like terms: 49 + -49 = 0 -49 + 15x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -49 + 15x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -49 + 15x + -1x2 = 0 + x2 + -1x2 -49 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -49 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 49 + -15x + x2 = 0 Move the constant term to the right: Add '-49' to each side of the equation. 49 + -15x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -15x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -15x + x2 = 0 + -49 -15x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -15x + x2 = -49 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 = -49 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -49 + 56.25 Combine like terms: -49 + 56.25 = 7.25 56.25 + -15x + x2 = 7.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -7.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -7.5 = 2.692582404 Simplifying x + -7.5 = 2.692582404 Reorder the terms: -7.5 + x = 2.692582404 Solving -7.5 + x = 2.692582404 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 = 2.692582404 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 2.692582404 + 7.5 x = 2.692582404 + 7.5 Combine like terms: 2.692582404 + 7.5 = 10.192582404 x = 10.192582404 Simplifying x = 10.192582404Subproblem 2
x + -7.5 = -2.692582404 Simplifying x + -7.5 = -2.692582404 Reorder the terms: -7.5 + x = -2.692582404 Solving -7.5 + x = -2.692582404 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 = -2.692582404 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -2.692582404 + 7.5 x = -2.692582404 + 7.5 Combine like terms: -2.692582404 + 7.5 = 4.807417596 x = 4.807417596 Simplifying x = 4.807417596Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.192582404, 4.807417596}
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