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Simplifying x2 + -4x = 42 Reorder the terms: -4x + x2 = 42 Solving -4x + x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + -4x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -4x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -4x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -4x + x2 = 0 + 42 -4x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -4x + x2 = 42 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 42 + 4 Reorder the terms: 4 + -4x + x2 = 42 + 4 Combine like terms: 42 + 4 = 46 4 + -4x + x2 = 46 Factor a perfect square on the left side: (x + -2)(x + -2) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -2) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -2 = 6.782329983 Simplifying x + -2 = 6.782329983 Reorder the terms: -2 + x = 6.782329983 Solving -2 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6.782329983 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.782329983 + 2 x = 6.782329983 + 2 Combine like terms: 6.782329983 + 2 = 8.782329983 x = 8.782329983 Simplifying x = 8.782329983Subproblem 2
x + -2 = -6.782329983 Simplifying x + -2 = -6.782329983 Reorder the terms: -2 + x = -6.782329983 Solving -2 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6.782329983 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.782329983 + 2 x = -6.782329983 + 2 Combine like terms: -6.782329983 + 2 = -4.782329983 x = -4.782329983 Simplifying x = -4.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.782329983, -4.782329983}
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