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Simplifying x2 + 10x + 21 = 529 Reorder the terms: 21 + 10x + x2 = 529 Solving 21 + 10x + x2 = 529 Solving for variable 'x'. Reorder the terms: 21 + -529 + 10x + x2 = 529 + -529 Combine like terms: 21 + -529 = -508 -508 + 10x + x2 = 529 + -529 Combine like terms: 529 + -529 = 0 -508 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '508' to each side of the equation. -508 + 10x + 508 + x2 = 0 + 508 Reorder the terms: -508 + 508 + 10x + x2 = 0 + 508 Combine like terms: -508 + 508 = 0 0 + 10x + x2 = 0 + 508 10x + x2 = 0 + 508 Combine like terms: 0 + 508 = 508 10x + x2 = 508 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 = 508 + 25 Reorder the terms: 25 + 10x + x2 = 508 + 25 Combine like terms: 508 + 25 = 533 25 + 10x + x2 = 533 Factor a perfect square on the left side: (x + 5)(x + 5) = 533 Calculate the square root of the right side: 23.086792761 Break this problem into two subproblems by setting (x + 5) equal to 23.086792761 and -23.086792761.Subproblem 1
x + 5 = 23.086792761 Simplifying x + 5 = 23.086792761 Reorder the terms: 5 + x = 23.086792761 Solving 5 + x = 23.086792761 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 = 23.086792761 + -5 Combine like terms: 5 + -5 = 0 0 + x = 23.086792761 + -5 x = 23.086792761 + -5 Combine like terms: 23.086792761 + -5 = 18.086792761 x = 18.086792761 Simplifying x = 18.086792761Subproblem 2
x + 5 = -23.086792761 Simplifying x + 5 = -23.086792761 Reorder the terms: 5 + x = -23.086792761 Solving 5 + x = -23.086792761 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 = -23.086792761 + -5 Combine like terms: 5 + -5 = 0 0 + x = -23.086792761 + -5 x = -23.086792761 + -5 Combine like terms: -23.086792761 + -5 = -28.086792761 x = -28.086792761 Simplifying x = -28.086792761Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.086792761, -28.086792761}
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