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Simplifying x2 + -2x + -155 = 0 Reorder the terms: -155 + -2x + x2 = 0 Solving -155 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + -2x + 155 + x2 = 0 + 155 Reorder the terms: -155 + 155 + -2x + x2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + -2x + x2 = 0 + 155 -2x + x2 = 0 + 155 Combine like terms: 0 + 155 = 155 -2x + x2 = 155 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 155 + 1 Reorder the terms: 1 + -2x + x2 = 155 + 1 Combine like terms: 155 + 1 = 156 1 + -2x + x2 = 156 Factor a perfect square on the left side: (x + -1)(x + -1) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -1) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -1 = 12.489995997 Simplifying x + -1 = 12.489995997 Reorder the terms: -1 + x = 12.489995997 Solving -1 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 12.489995997 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.489995997 + 1 x = 12.489995997 + 1 Combine like terms: 12.489995997 + 1 = 13.489995997 x = 13.489995997 Simplifying x = 13.489995997Subproblem 2
x + -1 = -12.489995997 Simplifying x + -1 = -12.489995997 Reorder the terms: -1 + x = -12.489995997 Solving -1 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -12.489995997 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.489995997 + 1 x = -12.489995997 + 1 Combine like terms: -12.489995997 + 1 = -11.489995997 x = -11.489995997 Simplifying x = -11.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.489995997, -11.489995997}
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