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Simplifying x2 + -1 = 14x + 5 Reorder the terms: -1 + x2 = 14x + 5 Reorder the terms: -1 + x2 = 5 + 14x Solving -1 + x2 = 5 + 14x Solving for variable 'x'. Reorder the terms: -1 + -5 + -14x + x2 = 5 + 14x + -5 + -14x Combine like terms: -1 + -5 = -6 -6 + -14x + x2 = 5 + 14x + -5 + -14x Reorder the terms: -6 + -14x + x2 = 5 + -5 + 14x + -14x Combine like terms: 5 + -5 = 0 -6 + -14x + x2 = 0 + 14x + -14x -6 + -14x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -6 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -14x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -14x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -14x + x2 = 0 + 6 -14x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -14x + x2 = 6 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 = 6 + 49 Reorder the terms: 49 + -14x + x2 = 6 + 49 Combine like terms: 6 + 49 = 55 49 + -14x + x2 = 55 Factor a perfect square on the left side: (x + -7)(x + -7) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -7) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -7 = 7.416198487 Simplifying x + -7 = 7.416198487 Reorder the terms: -7 + x = 7.416198487 Solving -7 + x = 7.416198487 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 = 7.416198487 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.416198487 + 7 x = 7.416198487 + 7 Combine like terms: 7.416198487 + 7 = 14.416198487 x = 14.416198487 Simplifying x = 14.416198487Subproblem 2
x + -7 = -7.416198487 Simplifying x + -7 = -7.416198487 Reorder the terms: -7 + x = -7.416198487 Solving -7 + x = -7.416198487 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 = -7.416198487 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.416198487 + 7 x = -7.416198487 + 7 Combine like terms: -7.416198487 + 7 = -0.416198487 x = -0.416198487 Simplifying x = -0.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.416198487, -0.416198487}
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