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Simplifying x2 + 44x + 316 = 0 Reorder the terms: 316 + 44x + x2 = 0 Solving 316 + 44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-316' to each side of the equation. 316 + 44x + -316 + x2 = 0 + -316 Reorder the terms: 316 + -316 + 44x + x2 = 0 + -316 Combine like terms: 316 + -316 = 0 0 + 44x + x2 = 0 + -316 44x + x2 = 0 + -316 Combine like terms: 0 + -316 = -316 44x + x2 = -316 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 = -316 + 484 Reorder the terms: 484 + 44x + x2 = -316 + 484 Combine like terms: -316 + 484 = 168 484 + 44x + x2 = 168 Factor a perfect square on the left side: (x + 22)(x + 22) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + 22) equal to 12.961481397 and -12.961481397.Subproblem 1
x + 22 = 12.961481397 Simplifying x + 22 = 12.961481397 Reorder the terms: 22 + x = 12.961481397 Solving 22 + x = 12.961481397 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 = 12.961481397 + -22 Combine like terms: 22 + -22 = 0 0 + x = 12.961481397 + -22 x = 12.961481397 + -22 Combine like terms: 12.961481397 + -22 = -9.038518603 x = -9.038518603 Simplifying x = -9.038518603Subproblem 2
x + 22 = -12.961481397 Simplifying x + 22 = -12.961481397 Reorder the terms: 22 + x = -12.961481397 Solving 22 + x = -12.961481397 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 = -12.961481397 + -22 Combine like terms: 22 + -22 = 0 0 + x = -12.961481397 + -22 x = -12.961481397 + -22 Combine like terms: -12.961481397 + -22 = -34.961481397 x = -34.961481397 Simplifying x = -34.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.038518603, -34.961481397}
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