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Simplifying x2 + -2x + 45 + -100 = 0 Reorder the terms: 45 + -100 + -2x + x2 = 0 Combine like terms: 45 + -100 = -55 -55 + -2x + x2 = 0 Solving -55 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -2x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -2x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -2x + x2 = 0 + 55 -2x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -2x + x2 = 55 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 = 55 + 1 Reorder the terms: 1 + -2x + x2 = 55 + 1 Combine like terms: 55 + 1 = 56 1 + -2x + x2 = 56 Factor a perfect square on the left side: (x + -1)(x + -1) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -1) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -1 = 7.483314774 Simplifying x + -1 = 7.483314774 Reorder the terms: -1 + x = 7.483314774 Solving -1 + x = 7.483314774 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 = 7.483314774 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.483314774 + 1 x = 7.483314774 + 1 Combine like terms: 7.483314774 + 1 = 8.483314774 x = 8.483314774 Simplifying x = 8.483314774Subproblem 2
x + -1 = -7.483314774 Simplifying x + -1 = -7.483314774 Reorder the terms: -1 + x = -7.483314774 Solving -1 + x = -7.483314774 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 = -7.483314774 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.483314774 + 1 x = -7.483314774 + 1 Combine like terms: -7.483314774 + 1 = -6.483314774 x = -6.483314774 Simplifying x = -6.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.483314774, -6.483314774}
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