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Simplifying x2 + 28x + 1 = 0 Reorder the terms: 1 + 28x + x2 = 0 Solving 1 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 28x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 28x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 28x + x2 = 0 + -1 28x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 28x + x2 = -1 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 = -1 + 196 Reorder the terms: 196 + 28x + x2 = -1 + 196 Combine like terms: -1 + 196 = 195 196 + 28x + x2 = 195 Factor a perfect square on the left side: (x + 14)(x + 14) = 195 Calculate the square root of the right side: 13.964240044 Break this problem into two subproblems by setting (x + 14) equal to 13.964240044 and -13.964240044.Subproblem 1
x + 14 = 13.964240044 Simplifying x + 14 = 13.964240044 Reorder the terms: 14 + x = 13.964240044 Solving 14 + x = 13.964240044 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 = 13.964240044 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.964240044 + -14 x = 13.964240044 + -14 Combine like terms: 13.964240044 + -14 = -0.035759956 x = -0.035759956 Simplifying x = -0.035759956Subproblem 2
x + 14 = -13.964240044 Simplifying x + 14 = -13.964240044 Reorder the terms: 14 + x = -13.964240044 Solving 14 + x = -13.964240044 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 = -13.964240044 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.964240044 + -14 x = -13.964240044 + -14 Combine like terms: -13.964240044 + -14 = -27.964240044 x = -27.964240044 Simplifying x = -27.964240044Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.035759956, -27.964240044}
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