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Simplifying x2 + 14x = 6 Reorder the terms: 14x + x2 = 6 Solving 14x + x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 14x + x2 = 6 + -6 Combine like terms: 6 + -6 = 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 = 0.416198487 x = 0.416198487 Simplifying x = 0.416198487Subproblem 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 = -14.416198487 x = -14.416198487 Simplifying x = -14.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.416198487, -14.416198487}
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