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Simplifying x2 + -2x + -34 = 0 Reorder the terms: -34 + -2x + x2 = 0 Solving -34 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -2x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -2x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -2x + x2 = 0 + 34 -2x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -2x + x2 = 34 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 = 34 + 1 Reorder the terms: 1 + -2x + x2 = 34 + 1 Combine like terms: 34 + 1 = 35 1 + -2x + x2 = 35 Factor a perfect square on the left side: (x + -1)(x + -1) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -1) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -1 = 5.916079783 Simplifying x + -1 = 5.916079783 Reorder the terms: -1 + x = 5.916079783 Solving -1 + x = 5.916079783 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 = 5.916079783 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.916079783 + 1 x = 5.916079783 + 1 Combine like terms: 5.916079783 + 1 = 6.916079783 x = 6.916079783 Simplifying x = 6.916079783Subproblem 2
x + -1 = -5.916079783 Simplifying x + -1 = -5.916079783 Reorder the terms: -1 + x = -5.916079783 Solving -1 + x = -5.916079783 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 = -5.916079783 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.916079783 + 1 x = -5.916079783 + 1 Combine like terms: -5.916079783 + 1 = -4.916079783 x = -4.916079783 Simplifying x = -4.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.916079783, -4.916079783}
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