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Simplifying x2 + 28x + 34 = 0 Reorder the terms: 34 + 28x + x2 = 0 Solving 34 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 28x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 28x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 28x + x2 = 0 + -34 28x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 28x + x2 = -34 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -34 + 196 Reorder the terms: 196 + 28x + x2 = -34 + 196 Combine like terms: -34 + 196 = 162 196 + 28x + x2 = 162 Factor a perfect square on the left side: (x + 14)(x + 14) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + 14) equal to 12.727922061 and -12.727922061.Subproblem 1
x + 14 = 12.727922061 Simplifying x + 14 = 12.727922061 Reorder the terms: 14 + x = 12.727922061 Solving 14 + x = 12.727922061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 12.727922061 + -14 Combine like terms: 14 + -14 = 0 0 + x = 12.727922061 + -14 x = 12.727922061 + -14 Combine like terms: 12.727922061 + -14 = -1.272077939 x = -1.272077939 Simplifying x = -1.272077939Subproblem 2
x + 14 = -12.727922061 Simplifying x + 14 = -12.727922061 Reorder the terms: 14 + x = -12.727922061 Solving 14 + x = -12.727922061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -12.727922061 + -14 Combine like terms: 14 + -14 = 0 0 + x = -12.727922061 + -14 x = -12.727922061 + -14 Combine like terms: -12.727922061 + -14 = -26.727922061 x = -26.727922061 Simplifying x = -26.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.272077939, -26.727922061}
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