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Simplifying x2 + 42x + 355 = 0 Reorder the terms: 355 + 42x + x2 = 0 Solving 355 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-355' to each side of the equation. 355 + 42x + -355 + x2 = 0 + -355 Reorder the terms: 355 + -355 + 42x + x2 = 0 + -355 Combine like terms: 355 + -355 = 0 0 + 42x + x2 = 0 + -355 42x + x2 = 0 + -355 Combine like terms: 0 + -355 = -355 42x + x2 = -355 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = -355 + 441 Reorder the terms: 441 + 42x + x2 = -355 + 441 Combine like terms: -355 + 441 = 86 441 + 42x + x2 = 86 Factor a perfect square on the left side: (x + 21)(x + 21) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 21) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 21 = 9.273618495 Simplifying x + 21 = 9.273618495 Reorder the terms: 21 + x = 9.273618495 Solving 21 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 9.273618495 + -21 Combine like terms: 21 + -21 = 0 0 + x = 9.273618495 + -21 x = 9.273618495 + -21 Combine like terms: 9.273618495 + -21 = -11.726381505 x = -11.726381505 Simplifying x = -11.726381505Subproblem 2
x + 21 = -9.273618495 Simplifying x + 21 = -9.273618495 Reorder the terms: 21 + x = -9.273618495 Solving 21 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -9.273618495 + -21 Combine like terms: 21 + -21 = 0 0 + x = -9.273618495 + -21 x = -9.273618495 + -21 Combine like terms: -9.273618495 + -21 = -30.273618495 x = -30.273618495 Simplifying x = -30.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.726381505, -30.273618495}
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