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Simplifying x2 + 10x + 21 = 1024 Reorder the terms: 21 + 10x + x2 = 1024 Solving 21 + 10x + x2 = 1024 Solving for variable 'x'. Reorder the terms: 21 + -1024 + 10x + x2 = 1024 + -1024 Combine like terms: 21 + -1024 = -1003 -1003 + 10x + x2 = 1024 + -1024 Combine like terms: 1024 + -1024 = 0 -1003 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1003' to each side of the equation. -1003 + 10x + 1003 + x2 = 0 + 1003 Reorder the terms: -1003 + 1003 + 10x + x2 = 0 + 1003 Combine like terms: -1003 + 1003 = 0 0 + 10x + x2 = 0 + 1003 10x + x2 = 0 + 1003 Combine like terms: 0 + 1003 = 1003 10x + x2 = 1003 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 1003 + 25 Reorder the terms: 25 + 10x + x2 = 1003 + 25 Combine like terms: 1003 + 25 = 1028 25 + 10x + x2 = 1028 Factor a perfect square on the left side: (x + 5)(x + 5) = 1028 Calculate the square root of the right side: 32.062439084 Break this problem into two subproblems by setting (x + 5) equal to 32.062439084 and -32.062439084.Subproblem 1
x + 5 = 32.062439084 Simplifying x + 5 = 32.062439084 Reorder the terms: 5 + x = 32.062439084 Solving 5 + x = 32.062439084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 32.062439084 + -5 Combine like terms: 5 + -5 = 0 0 + x = 32.062439084 + -5 x = 32.062439084 + -5 Combine like terms: 32.062439084 + -5 = 27.062439084 x = 27.062439084 Simplifying x = 27.062439084Subproblem 2
x + 5 = -32.062439084 Simplifying x + 5 = -32.062439084 Reorder the terms: 5 + x = -32.062439084 Solving 5 + x = -32.062439084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -32.062439084 + -5 Combine like terms: 5 + -5 = 0 0 + x = -32.062439084 + -5 x = -32.062439084 + -5 Combine like terms: -32.062439084 + -5 = -37.062439084 x = -37.062439084 Simplifying x = -37.062439084Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.062439084, -37.062439084}
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