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Simplifying x2 + 28x + 19 = 0 Reorder the terms: 19 + 28x + x2 = 0 Solving 19 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 28x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 28x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 28x + x2 = 0 + -19 28x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 28x + x2 = -19 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 = -19 + 196 Reorder the terms: 196 + 28x + x2 = -19 + 196 Combine like terms: -19 + 196 = 177 196 + 28x + x2 = 177 Factor a perfect square on the left side: (x + 14)(x + 14) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + 14) equal to 13.304134696 and -13.304134696.Subproblem 1
x + 14 = 13.304134696 Simplifying x + 14 = 13.304134696 Reorder the terms: 14 + x = 13.304134696 Solving 14 + x = 13.304134696 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 = 13.304134696 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.304134696 + -14 x = 13.304134696 + -14 Combine like terms: 13.304134696 + -14 = -0.695865304 x = -0.695865304 Simplifying x = -0.695865304Subproblem 2
x + 14 = -13.304134696 Simplifying x + 14 = -13.304134696 Reorder the terms: 14 + x = -13.304134696 Solving 14 + x = -13.304134696 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 = -13.304134696 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.304134696 + -14 x = -13.304134696 + -14 Combine like terms: -13.304134696 + -14 = -27.304134696 x = -27.304134696 Simplifying x = -27.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.695865304, -27.304134696}
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