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Simplifying x2 + 28x + 54 = 0 Reorder the terms: 54 + 28x + x2 = 0 Solving 54 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + 28x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + 28x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 28x + x2 = 0 + -54 28x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 28x + x2 = -54 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 = -54 + 196 Reorder the terms: 196 + 28x + x2 = -54 + 196 Combine like terms: -54 + 196 = 142 196 + 28x + x2 = 142 Factor a perfect square on the left side: (x + 14)(x + 14) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (x + 14) equal to 11.916375288 and -11.916375288.Subproblem 1
x + 14 = 11.916375288 Simplifying x + 14 = 11.916375288 Reorder the terms: 14 + x = 11.916375288 Solving 14 + x = 11.916375288 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 = 11.916375288 + -14 Combine like terms: 14 + -14 = 0 0 + x = 11.916375288 + -14 x = 11.916375288 + -14 Combine like terms: 11.916375288 + -14 = -2.083624712 x = -2.083624712 Simplifying x = -2.083624712Subproblem 2
x + 14 = -11.916375288 Simplifying x + 14 = -11.916375288 Reorder the terms: 14 + x = -11.916375288 Solving 14 + x = -11.916375288 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 = -11.916375288 + -14 Combine like terms: 14 + -14 = 0 0 + x = -11.916375288 + -14 x = -11.916375288 + -14 Combine like terms: -11.916375288 + -14 = -25.916375288 x = -25.916375288 Simplifying x = -25.916375288Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.083624712, -25.916375288}
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