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Simplifying x2 + -2x + -51 = 0 Reorder the terms: -51 + -2x + x2 = 0 Solving -51 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -2x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -2x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -2x + x2 = 0 + 51 -2x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -2x + x2 = 51 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 = 51 + 1 Reorder the terms: 1 + -2x + x2 = 51 + 1 Combine like terms: 51 + 1 = 52 1 + -2x + x2 = 52 Factor a perfect square on the left side: (x + -1)(x + -1) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -1) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -1 = 7.211102551 Simplifying x + -1 = 7.211102551 Reorder the terms: -1 + x = 7.211102551 Solving -1 + x = 7.211102551 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 = 7.211102551 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.211102551 + 1 x = 7.211102551 + 1 Combine like terms: 7.211102551 + 1 = 8.211102551 x = 8.211102551 Simplifying x = 8.211102551Subproblem 2
x + -1 = -7.211102551 Simplifying x + -1 = -7.211102551 Reorder the terms: -1 + x = -7.211102551 Solving -1 + x = -7.211102551 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 = -7.211102551 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.211102551 + 1 x = -7.211102551 + 1 Combine like terms: -7.211102551 + 1 = -6.211102551 x = -6.211102551 Simplifying x = -6.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.211102551, -6.211102551}
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