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Simplifying x2 + -44x + 300 = 0 Reorder the terms: 300 + -44x + x2 = 0 Solving 300 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -44x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -44x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -44x + x2 = 0 + -300 -44x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -44x + x2 = -300 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 = -300 + 484 Reorder the terms: 484 + -44x + x2 = -300 + 484 Combine like terms: -300 + 484 = 184 484 + -44x + x2 = 184 Factor a perfect square on the left side: (x + -22)(x + -22) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + -22) equal to 13.564659966 and -13.564659966.Subproblem 1
x + -22 = 13.564659966 Simplifying x + -22 = 13.564659966 Reorder the terms: -22 + x = 13.564659966 Solving -22 + x = 13.564659966 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 = 13.564659966 + 22 Combine like terms: -22 + 22 = 0 0 + x = 13.564659966 + 22 x = 13.564659966 + 22 Combine like terms: 13.564659966 + 22 = 35.564659966 x = 35.564659966 Simplifying x = 35.564659966Subproblem 2
x + -22 = -13.564659966 Simplifying x + -22 = -13.564659966 Reorder the terms: -22 + x = -13.564659966 Solving -22 + x = -13.564659966 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 = -13.564659966 + 22 Combine like terms: -22 + 22 = 0 0 + x = -13.564659966 + 22 x = -13.564659966 + 22 Combine like terms: -13.564659966 + 22 = 8.435340034 x = 8.435340034 Simplifying x = 8.435340034Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.564659966, 8.435340034}
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