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Simplifying x2 + -14x + -49 = 16 Reorder the terms: -49 + -14x + x2 = 16 Solving -49 + -14x + x2 = 16 Solving for variable 'x'. Reorder the terms: -49 + -16 + -14x + x2 = 16 + -16 Combine like terms: -49 + -16 = -65 -65 + -14x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -65 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -14x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -14x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -14x + x2 = 0 + 65 -14x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -14x + x2 = 65 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 = 65 + 49 Reorder the terms: 49 + -14x + x2 = 65 + 49 Combine like terms: 65 + 49 = 114 49 + -14x + x2 = 114 Factor a perfect square on the left side: (x + -7)(x + -7) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + -7) equal to 10.677078252 and -10.677078252.Subproblem 1
x + -7 = 10.677078252 Simplifying x + -7 = 10.677078252 Reorder the terms: -7 + x = 10.677078252 Solving -7 + x = 10.677078252 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 = 10.677078252 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.677078252 + 7 x = 10.677078252 + 7 Combine like terms: 10.677078252 + 7 = 17.677078252 x = 17.677078252 Simplifying x = 17.677078252Subproblem 2
x + -7 = -10.677078252 Simplifying x + -7 = -10.677078252 Reorder the terms: -7 + x = -10.677078252 Solving -7 + x = -10.677078252 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 = -10.677078252 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.677078252 + 7 x = -10.677078252 + 7 Combine like terms: -10.677078252 + 7 = -3.677078252 x = -3.677078252 Simplifying x = -3.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.677078252, -3.677078252}
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