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Simplifying x2 + -2x + -5 = 42 Reorder the terms: -5 + -2x + x2 = 42 Solving -5 + -2x + x2 = 42 Solving for variable 'x'. Reorder the terms: -5 + -42 + -2x + x2 = 42 + -42 Combine like terms: -5 + -42 = -47 -47 + -2x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -47 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -2x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + -2x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2x + x2 = 0 + 47 -2x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 -2x + x2 = 47 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 = 47 + 1 Reorder the terms: 1 + -2x + x2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + -2x + x2 = 48 Factor a perfect square on the left side: (x + -1)(x + -1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -1) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -1 = 6.92820323 Simplifying x + -1 = 6.92820323 Reorder the terms: -1 + x = 6.92820323 Solving -1 + x = 6.92820323 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 = 6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.92820323 + 1 x = 6.92820323 + 1 Combine like terms: 6.92820323 + 1 = 7.92820323 x = 7.92820323 Simplifying x = 7.92820323Subproblem 2
x + -1 = -6.92820323 Simplifying x + -1 = -6.92820323 Reorder the terms: -1 + x = -6.92820323 Solving -1 + x = -6.92820323 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 = -6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.92820323 + 1 x = -6.92820323 + 1 Combine like terms: -6.92820323 + 1 = -5.92820323 x = -5.92820323 Simplifying x = -5.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.92820323, -5.92820323}
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