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Simplifying x2 + 14x + -272 = 0 Reorder the terms: -272 + 14x + x2 = 0 Solving -272 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '272' to each side of the equation. -272 + 14x + 272 + x2 = 0 + 272 Reorder the terms: -272 + 272 + 14x + x2 = 0 + 272 Combine like terms: -272 + 272 = 0 0 + 14x + x2 = 0 + 272 14x + x2 = 0 + 272 Combine like terms: 0 + 272 = 272 14x + x2 = 272 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 = 272 + 49 Reorder the terms: 49 + 14x + x2 = 272 + 49 Combine like terms: 272 + 49 = 321 49 + 14x + x2 = 321 Factor a perfect square on the left side: (x + 7)(x + 7) = 321 Calculate the square root of the right side: 17.916472867 Break this problem into two subproblems by setting (x + 7) equal to 17.916472867 and -17.916472867.Subproblem 1
x + 7 = 17.916472867 Simplifying x + 7 = 17.916472867 Reorder the terms: 7 + x = 17.916472867 Solving 7 + x = 17.916472867 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 = 17.916472867 + -7 Combine like terms: 7 + -7 = 0 0 + x = 17.916472867 + -7 x = 17.916472867 + -7 Combine like terms: 17.916472867 + -7 = 10.916472867 x = 10.916472867 Simplifying x = 10.916472867Subproblem 2
x + 7 = -17.916472867 Simplifying x + 7 = -17.916472867 Reorder the terms: 7 + x = -17.916472867 Solving 7 + x = -17.916472867 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 = -17.916472867 + -7 Combine like terms: 7 + -7 = 0 0 + x = -17.916472867 + -7 x = -17.916472867 + -7 Combine like terms: -17.916472867 + -7 = -24.916472867 x = -24.916472867 Simplifying x = -24.916472867Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.916472867, -24.916472867}
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