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Simplifying x2 + -2x + -78 = 0 Reorder the terms: -78 + -2x + x2 = 0 Solving -78 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -2x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -2x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -2x + x2 = 0 + 78 -2x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -2x + x2 = 78 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 = 78 + 1 Reorder the terms: 1 + -2x + x2 = 78 + 1 Combine like terms: 78 + 1 = 79 1 + -2x + x2 = 79 Factor a perfect square on the left side: (x + -1)(x + -1) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -1) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -1 = 8.888194417 Simplifying x + -1 = 8.888194417 Reorder the terms: -1 + x = 8.888194417 Solving -1 + x = 8.888194417 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 = 8.888194417 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.888194417 + 1 x = 8.888194417 + 1 Combine like terms: 8.888194417 + 1 = 9.888194417 x = 9.888194417 Simplifying x = 9.888194417Subproblem 2
x + -1 = -8.888194417 Simplifying x + -1 = -8.888194417 Reorder the terms: -1 + x = -8.888194417 Solving -1 + x = -8.888194417 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 = -8.888194417 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.888194417 + 1 x = -8.888194417 + 1 Combine like terms: -8.888194417 + 1 = -7.888194417 x = -7.888194417 Simplifying x = -7.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.888194417, -7.888194417}
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