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Simplifying x2 + -4x + -171 = 0 Reorder the terms: -171 + -4x + x2 = 0 Solving -171 + -4x + 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 + -4x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + -4x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + -4x + x2 = 0 + 171 -4x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 -4x + x2 = 171 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 171 + 4 Reorder the terms: 4 + -4x + x2 = 171 + 4 Combine like terms: 171 + 4 = 175 4 + -4x + x2 = 175 Factor a perfect square on the left side: (x + -2)(x + -2) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -2) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -2 = 13.228756555 Simplifying x + -2 = 13.228756555 Reorder the terms: -2 + x = 13.228756555 Solving -2 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 13.228756555 + 2 Combine like terms: -2 + 2 = 0 0 + x = 13.228756555 + 2 x = 13.228756555 + 2 Combine like terms: 13.228756555 + 2 = 15.228756555 x = 15.228756555 Simplifying x = 15.228756555Subproblem 2
x + -2 = -13.228756555 Simplifying x + -2 = -13.228756555 Reorder the terms: -2 + x = -13.228756555 Solving -2 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -13.228756555 + 2 Combine like terms: -2 + 2 = 0 0 + x = -13.228756555 + 2 x = -13.228756555 + 2 Combine like terms: -13.228756555 + 2 = -11.228756555 x = -11.228756555 Simplifying x = -11.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.228756555, -11.228756555}
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