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Simplifying x2 + 2x + -678 = 0 Reorder the terms: -678 + 2x + x2 = 0 Solving -678 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '678' to each side of the equation. -678 + 2x + 678 + x2 = 0 + 678 Reorder the terms: -678 + 678 + 2x + x2 = 0 + 678 Combine like terms: -678 + 678 = 0 0 + 2x + x2 = 0 + 678 2x + x2 = 0 + 678 Combine like terms: 0 + 678 = 678 2x + x2 = 678 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 = 678 + 1 Reorder the terms: 1 + 2x + x2 = 678 + 1 Combine like terms: 678 + 1 = 679 1 + 2x + x2 = 679 Factor a perfect square on the left side: (x + 1)(x + 1) = 679 Calculate the square root of the right side: 26.057628442 Break this problem into two subproblems by setting (x + 1) equal to 26.057628442 and -26.057628442.Subproblem 1
x + 1 = 26.057628442 Simplifying x + 1 = 26.057628442 Reorder the terms: 1 + x = 26.057628442 Solving 1 + x = 26.057628442 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 = 26.057628442 + -1 Combine like terms: 1 + -1 = 0 0 + x = 26.057628442 + -1 x = 26.057628442 + -1 Combine like terms: 26.057628442 + -1 = 25.057628442 x = 25.057628442 Simplifying x = 25.057628442Subproblem 2
x + 1 = -26.057628442 Simplifying x + 1 = -26.057628442 Reorder the terms: 1 + x = -26.057628442 Solving 1 + x = -26.057628442 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 = -26.057628442 + -1 Combine like terms: 1 + -1 = 0 0 + x = -26.057628442 + -1 x = -26.057628442 + -1 Combine like terms: -26.057628442 + -1 = -27.057628442 x = -27.057628442 Simplifying x = -27.057628442Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.057628442, -27.057628442}
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