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Simplifying x2 + 21x + -362 = 0 Reorder the terms: -362 + 21x + x2 = 0 Solving -362 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '362' to each side of the equation. -362 + 21x + 362 + x2 = 0 + 362 Reorder the terms: -362 + 362 + 21x + x2 = 0 + 362 Combine like terms: -362 + 362 = 0 0 + 21x + x2 = 0 + 362 21x + x2 = 0 + 362 Combine like terms: 0 + 362 = 362 21x + x2 = 362 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 362 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 362 + 110.25 Combine like terms: 362 + 110.25 = 472.25 110.25 + 21x + x2 = 472.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 472.25 Calculate the square root of the right side: 21.731313812 Break this problem into two subproblems by setting (x + 10.5) equal to 21.731313812 and -21.731313812.Subproblem 1
x + 10.5 = 21.731313812 Simplifying x + 10.5 = 21.731313812 Reorder the terms: 10.5 + x = 21.731313812 Solving 10.5 + x = 21.731313812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 21.731313812 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 21.731313812 + -10.5 x = 21.731313812 + -10.5 Combine like terms: 21.731313812 + -10.5 = 11.231313812 x = 11.231313812 Simplifying x = 11.231313812Subproblem 2
x + 10.5 = -21.731313812 Simplifying x + 10.5 = -21.731313812 Reorder the terms: 10.5 + x = -21.731313812 Solving 10.5 + x = -21.731313812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -21.731313812 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -21.731313812 + -10.5 x = -21.731313812 + -10.5 Combine like terms: -21.731313812 + -10.5 = -32.231313812 x = -32.231313812 Simplifying x = -32.231313812Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.231313812, -32.231313812}
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