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Simplifying x(x + -2) = 44 Reorder the terms: x(-2 + x) = 44 (-2 * x + x * x) = 44 (-2x + x2) = 44 Solving -2x + x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -2x + x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -2x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -2x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -2x + x2 = 0 + 44 -2x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -2x + x2 = 44 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 = 44 + 1 Reorder the terms: 1 + -2x + x2 = 44 + 1 Combine like terms: 44 + 1 = 45 1 + -2x + x2 = 45 Factor a perfect square on the left side: (x + -1)(x + -1) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -1) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -1 = 6.708203933 Simplifying x + -1 = 6.708203933 Reorder the terms: -1 + x = 6.708203933 Solving -1 + x = 6.708203933 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 = 6.708203933 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.708203933 + 1 x = 6.708203933 + 1 Combine like terms: 6.708203933 + 1 = 7.708203933 x = 7.708203933 Simplifying x = 7.708203933Subproblem 2
x + -1 = -6.708203933 Simplifying x + -1 = -6.708203933 Reorder the terms: -1 + x = -6.708203933 Solving -1 + x = -6.708203933 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 = -6.708203933 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.708203933 + 1 x = -6.708203933 + 1 Combine like terms: -6.708203933 + 1 = -5.708203933 x = -5.708203933 Simplifying x = -5.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.708203933, -5.708203933}
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