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Simplifying x2 + 44x + 477 = 0 Reorder the terms: 477 + 44x + x2 = 0 Solving 477 + 44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-477' to each side of the equation. 477 + 44x + -477 + x2 = 0 + -477 Reorder the terms: 477 + -477 + 44x + x2 = 0 + -477 Combine like terms: 477 + -477 = 0 0 + 44x + x2 = 0 + -477 44x + x2 = 0 + -477 Combine like terms: 0 + -477 = -477 44x + x2 = -477 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 = -477 + 484 Reorder the terms: 484 + 44x + x2 = -477 + 484 Combine like terms: -477 + 484 = 7 484 + 44x + x2 = 7 Factor a perfect square on the left side: (x + 22)(x + 22) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 22) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 22 = 2.645751311 Simplifying x + 22 = 2.645751311 Reorder the terms: 22 + x = 2.645751311 Solving 22 + x = 2.645751311 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 = 2.645751311 + -22 Combine like terms: 22 + -22 = 0 0 + x = 2.645751311 + -22 x = 2.645751311 + -22 Combine like terms: 2.645751311 + -22 = -19.354248689 x = -19.354248689 Simplifying x = -19.354248689Subproblem 2
x + 22 = -2.645751311 Simplifying x + 22 = -2.645751311 Reorder the terms: 22 + x = -2.645751311 Solving 22 + x = -2.645751311 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 = -2.645751311 + -22 Combine like terms: 22 + -22 = 0 0 + x = -2.645751311 + -22 x = -2.645751311 + -22 Combine like terms: -2.645751311 + -22 = -24.645751311 x = -24.645751311 Simplifying x = -24.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-19.354248689, -24.645751311}
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