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Simplifying x2 + 14x + -384 = 0 Reorder the terms: -384 + 14x + x2 = 0 Solving -384 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + 14x + 384 + x2 = 0 + 384 Reorder the terms: -384 + 384 + 14x + x2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + 14x + x2 = 0 + 384 14x + x2 = 0 + 384 Combine like terms: 0 + 384 = 384 14x + x2 = 384 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 = 384 + 49 Reorder the terms: 49 + 14x + x2 = 384 + 49 Combine like terms: 384 + 49 = 433 49 + 14x + x2 = 433 Factor a perfect square on the left side: (x + 7)(x + 7) = 433 Calculate the square root of the right side: 20.808652047 Break this problem into two subproblems by setting (x + 7) equal to 20.808652047 and -20.808652047.Subproblem 1
x + 7 = 20.808652047 Simplifying x + 7 = 20.808652047 Reorder the terms: 7 + x = 20.808652047 Solving 7 + x = 20.808652047 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 = 20.808652047 + -7 Combine like terms: 7 + -7 = 0 0 + x = 20.808652047 + -7 x = 20.808652047 + -7 Combine like terms: 20.808652047 + -7 = 13.808652047 x = 13.808652047 Simplifying x = 13.808652047Subproblem 2
x + 7 = -20.808652047 Simplifying x + 7 = -20.808652047 Reorder the terms: 7 + x = -20.808652047 Solving 7 + x = -20.808652047 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 = -20.808652047 + -7 Combine like terms: 7 + -7 = 0 0 + x = -20.808652047 + -7 x = -20.808652047 + -7 Combine like terms: -20.808652047 + -7 = -27.808652047 x = -27.808652047 Simplifying x = -27.808652047Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.808652047, -27.808652047}
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