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Simplifying x2 + 28x + -171 = 0 Reorder the terms: -171 + 28x + x2 = 0 Solving -171 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '171' to each side of the equation. -171 + 28x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + 28x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + 28x + x2 = 0 + 171 28x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 28x + x2 = 171 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 = 171 + 196 Reorder the terms: 196 + 28x + x2 = 171 + 196 Combine like terms: 171 + 196 = 367 196 + 28x + x2 = 367 Factor a perfect square on the left side: (x + 14)(x + 14) = 367 Calculate the square root of the right side: 19.157244061 Break this problem into two subproblems by setting (x + 14) equal to 19.157244061 and -19.157244061.Subproblem 1
x + 14 = 19.157244061 Simplifying x + 14 = 19.157244061 Reorder the terms: 14 + x = 19.157244061 Solving 14 + x = 19.157244061 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 = 19.157244061 + -14 Combine like terms: 14 + -14 = 0 0 + x = 19.157244061 + -14 x = 19.157244061 + -14 Combine like terms: 19.157244061 + -14 = 5.157244061 x = 5.157244061 Simplifying x = 5.157244061Subproblem 2
x + 14 = -19.157244061 Simplifying x + 14 = -19.157244061 Reorder the terms: 14 + x = -19.157244061 Solving 14 + x = -19.157244061 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 = -19.157244061 + -14 Combine like terms: 14 + -14 = 0 0 + x = -19.157244061 + -14 x = -19.157244061 + -14 Combine like terms: -19.157244061 + -14 = -33.157244061 x = -33.157244061 Simplifying x = -33.157244061Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.157244061, -33.157244061}
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