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Simplifying x2 + 42x + -48 = 0 Reorder the terms: -48 + 42x + x2 = 0 Solving -48 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 42x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 42x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 42x + x2 = 0 + 48 42x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 42x + x2 = 48 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 = 48 + 441 Reorder the terms: 441 + 42x + x2 = 48 + 441 Combine like terms: 48 + 441 = 489 441 + 42x + x2 = 489 Factor a perfect square on the left side: (x + 21)(x + 21) = 489 Calculate the square root of the right side: 22.113344387 Break this problem into two subproblems by setting (x + 21) equal to 22.113344387 and -22.113344387.Subproblem 1
x + 21 = 22.113344387 Simplifying x + 21 = 22.113344387 Reorder the terms: 21 + x = 22.113344387 Solving 21 + x = 22.113344387 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 = 22.113344387 + -21 Combine like terms: 21 + -21 = 0 0 + x = 22.113344387 + -21 x = 22.113344387 + -21 Combine like terms: 22.113344387 + -21 = 1.113344387 x = 1.113344387 Simplifying x = 1.113344387Subproblem 2
x + 21 = -22.113344387 Simplifying x + 21 = -22.113344387 Reorder the terms: 21 + x = -22.113344387 Solving 21 + x = -22.113344387 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 = -22.113344387 + -21 Combine like terms: 21 + -21 = 0 0 + x = -22.113344387 + -21 x = -22.113344387 + -21 Combine like terms: -22.113344387 + -21 = -43.113344387 x = -43.113344387 Simplifying x = -43.113344387Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.113344387, -43.113344387}
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