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Simplifying x2 + -14x = 7 Reorder the terms: -14x + x2 = 7 Solving -14x + x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -14x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -14x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -14x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -14x + x2 = 0 + 7 -14x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -14x + x2 = 7 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 7 + 49 Reorder the terms: 49 + -14x + x2 = 7 + 49 Combine like terms: 7 + 49 = 56 49 + -14x + x2 = 56 Factor a perfect square on the left side: (x + -7)(x + -7) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -7) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -7 = 7.483314774 Simplifying x + -7 = 7.483314774 Reorder the terms: -7 + x = 7.483314774 Solving -7 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.483314774 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.483314774 + 7 x = 7.483314774 + 7 Combine like terms: 7.483314774 + 7 = 14.483314774 x = 14.483314774 Simplifying x = 14.483314774Subproblem 2
x + -7 = -7.483314774 Simplifying x + -7 = -7.483314774 Reorder the terms: -7 + x = -7.483314774 Solving -7 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.483314774 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.483314774 + 7 x = -7.483314774 + 7 Combine like terms: -7.483314774 + 7 = -0.483314774 x = -0.483314774 Simplifying x = -0.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.483314774, -0.483314774}
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