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Simplifying x2 + 44x + -225 = 0 Reorder the terms: -225 + 44x + x2 = 0 Solving -225 + 44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 44x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 44x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 44x + x2 = 0 + 225 44x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 44x + x2 = 225 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 = 225 + 484 Reorder the terms: 484 + 44x + x2 = 225 + 484 Combine like terms: 225 + 484 = 709 484 + 44x + x2 = 709 Factor a perfect square on the left side: (x + 22)(x + 22) = 709 Calculate the square root of the right side: 26.627053911 Break this problem into two subproblems by setting (x + 22) equal to 26.627053911 and -26.627053911.Subproblem 1
x + 22 = 26.627053911 Simplifying x + 22 = 26.627053911 Reorder the terms: 22 + x = 26.627053911 Solving 22 + x = 26.627053911 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 = 26.627053911 + -22 Combine like terms: 22 + -22 = 0 0 + x = 26.627053911 + -22 x = 26.627053911 + -22 Combine like terms: 26.627053911 + -22 = 4.627053911 x = 4.627053911 Simplifying x = 4.627053911Subproblem 2
x + 22 = -26.627053911 Simplifying x + 22 = -26.627053911 Reorder the terms: 22 + x = -26.627053911 Solving 22 + x = -26.627053911 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 = -26.627053911 + -22 Combine like terms: 22 + -22 = 0 0 + x = -26.627053911 + -22 x = -26.627053911 + -22 Combine like terms: -26.627053911 + -22 = -48.627053911 x = -48.627053911 Simplifying x = -48.627053911Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.627053911, -48.627053911}
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