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Simplifying x2 + 14x + -51 = -7 Reorder the terms: -51 + 14x + x2 = -7 Solving -51 + 14x + x2 = -7 Solving for variable 'x'. Reorder the terms: -51 + 7 + 14x + x2 = -7 + 7 Combine like terms: -51 + 7 = -44 -44 + 14x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -44 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 14x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 14x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 14x + x2 = 0 + 44 14x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 14x + x2 = 44 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 = 44 + 49 Reorder the terms: 49 + 14x + x2 = 44 + 49 Combine like terms: 44 + 49 = 93 49 + 14x + x2 = 93 Factor a perfect square on the left side: (x + 7)(x + 7) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (x + 7) equal to 9.643650761 and -9.643650761.Subproblem 1
x + 7 = 9.643650761 Simplifying x + 7 = 9.643650761 Reorder the terms: 7 + x = 9.643650761 Solving 7 + x = 9.643650761 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 = 9.643650761 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.643650761 + -7 x = 9.643650761 + -7 Combine like terms: 9.643650761 + -7 = 2.643650761 x = 2.643650761 Simplifying x = 2.643650761Subproblem 2
x + 7 = -9.643650761 Simplifying x + 7 = -9.643650761 Reorder the terms: 7 + x = -9.643650761 Solving 7 + x = -9.643650761 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 = -9.643650761 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.643650761 + -7 x = -9.643650761 + -7 Combine like terms: -9.643650761 + -7 = -16.643650761 x = -16.643650761 Simplifying x = -16.643650761Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.643650761, -16.643650761}
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