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Simplifying (2 + x)(x + -1) = 42 Reorder the terms: (2 + x)(-1 + x) = 42 Multiply (2 + x) * (-1 + x) (2(-1 + x) + x(-1 + x)) = 42 ((-1 * 2 + x * 2) + x(-1 + x)) = 42 ((-2 + 2x) + x(-1 + x)) = 42 (-2 + 2x + (-1 * x + x * x)) = 42 (-2 + 2x + (-1x + x2)) = 42 Combine like terms: 2x + -1x = 1x (-2 + 1x + x2) = 42 Solving -2 + 1x + x2 = 42 Solving for variable 'x'. Reorder the terms: -2 + -42 + 1x + x2 = 42 + -42 Combine like terms: -2 + -42 = -44 -44 + 1x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -44 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 1x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 1x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 1x + x2 = 0 + 44 1x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 1x + x2 = 44 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 44 + 0.25 Reorder the terms: 0.25 + x + x2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 0.25 + x + x2 = 44.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 0.5 = 6.652067348 Simplifying x + 0.5 = 6.652067348 Reorder the terms: 0.5 + x = 6.652067348 Solving 0.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.652067348 + -0.5 x = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 x = 6.152067348 Simplifying x = 6.152067348Subproblem 2
x + 0.5 = -6.652067348 Simplifying x + 0.5 = -6.652067348 Reorder the terms: 0.5 + x = -6.652067348 Solving 0.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.652067348 + -0.5 x = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 x = -7.152067348 Simplifying x = -7.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.152067348, -7.152067348}
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