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Simplifying x2 + -44x + 45 = 0 Reorder the terms: 45 + -44x + x2 = 0 Solving 45 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -44x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -44x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -44x + x2 = 0 + -45 -44x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -44x + x2 = -45 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 = -45 + 484 Reorder the terms: 484 + -44x + x2 = -45 + 484 Combine like terms: -45 + 484 = 439 484 + -44x + x2 = 439 Factor a perfect square on the left side: (x + -22)(x + -22) = 439 Calculate the square root of the right side: 20.95232684 Break this problem into two subproblems by setting (x + -22) equal to 20.95232684 and -20.95232684.Subproblem 1
x + -22 = 20.95232684 Simplifying x + -22 = 20.95232684 Reorder the terms: -22 + x = 20.95232684 Solving -22 + x = 20.95232684 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 = 20.95232684 + 22 Combine like terms: -22 + 22 = 0 0 + x = 20.95232684 + 22 x = 20.95232684 + 22 Combine like terms: 20.95232684 + 22 = 42.95232684 x = 42.95232684 Simplifying x = 42.95232684Subproblem 2
x + -22 = -20.95232684 Simplifying x + -22 = -20.95232684 Reorder the terms: -22 + x = -20.95232684 Solving -22 + x = -20.95232684 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 = -20.95232684 + 22 Combine like terms: -22 + 22 = 0 0 + x = -20.95232684 + 22 x = -20.95232684 + 22 Combine like terms: -20.95232684 + 22 = 1.04767316 x = 1.04767316 Simplifying x = 1.04767316Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.95232684, 1.04767316}
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