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Simplifying x2 + -44x + 41 = 0 Reorder the terms: 41 + -44x + x2 = 0 Solving 41 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -44x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -44x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -44x + x2 = 0 + -41 -44x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -44x + x2 = -41 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -41 + 484 Reorder the terms: 484 + -44x + x2 = -41 + 484 Combine like terms: -41 + 484 = 443 484 + -44x + x2 = 443 Factor a perfect square on the left side: (x + -22)(x + -22) = 443 Calculate the square root of the right side: 21.04756518 Break this problem into two subproblems by setting (x + -22) equal to 21.04756518 and -21.04756518.Subproblem 1
x + -22 = 21.04756518 Simplifying x + -22 = 21.04756518 Reorder the terms: -22 + x = 21.04756518 Solving -22 + x = 21.04756518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 21.04756518 + 22 Combine like terms: -22 + 22 = 0 0 + x = 21.04756518 + 22 x = 21.04756518 + 22 Combine like terms: 21.04756518 + 22 = 43.04756518 x = 43.04756518 Simplifying x = 43.04756518Subproblem 2
x + -22 = -21.04756518 Simplifying x + -22 = -21.04756518 Reorder the terms: -22 + x = -21.04756518 Solving -22 + x = -21.04756518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -21.04756518 + 22 Combine like terms: -22 + 22 = 0 0 + x = -21.04756518 + 22 x = -21.04756518 + 22 Combine like terms: -21.04756518 + 22 = 0.95243482 x = 0.95243482 Simplifying x = 0.95243482Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.04756518, 0.95243482}
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