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Simplifying x2 + -2x + -340 = 0 Reorder the terms: -340 + -2x + x2 = 0 Solving -340 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + -2x + 340 + x2 = 0 + 340 Reorder the terms: -340 + 340 + -2x + x2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + -2x + x2 = 0 + 340 -2x + x2 = 0 + 340 Combine like terms: 0 + 340 = 340 -2x + x2 = 340 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 = 340 + 1 Reorder the terms: 1 + -2x + x2 = 340 + 1 Combine like terms: 340 + 1 = 341 1 + -2x + x2 = 341 Factor a perfect square on the left side: (x + -1)(x + -1) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + -1) equal to 18.466185313 and -18.466185313.Subproblem 1
x + -1 = 18.466185313 Simplifying x + -1 = 18.466185313 Reorder the terms: -1 + x = 18.466185313 Solving -1 + x = 18.466185313 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 = 18.466185313 + 1 Combine like terms: -1 + 1 = 0 0 + x = 18.466185313 + 1 x = 18.466185313 + 1 Combine like terms: 18.466185313 + 1 = 19.466185313 x = 19.466185313 Simplifying x = 19.466185313Subproblem 2
x + -1 = -18.466185313 Simplifying x + -1 = -18.466185313 Reorder the terms: -1 + x = -18.466185313 Solving -1 + x = -18.466185313 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 = -18.466185313 + 1 Combine like terms: -1 + 1 = 0 0 + x = -18.466185313 + 1 x = -18.466185313 + 1 Combine like terms: -18.466185313 + 1 = -17.466185313 x = -17.466185313 Simplifying x = -17.466185313Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.466185313, -17.466185313}
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