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Simplifying x2 + 10x + -1232 = 0 Reorder the terms: -1232 + 10x + x2 = 0 Solving -1232 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1232' to each side of the equation. -1232 + 10x + 1232 + x2 = 0 + 1232 Reorder the terms: -1232 + 1232 + 10x + x2 = 0 + 1232 Combine like terms: -1232 + 1232 = 0 0 + 10x + x2 = 0 + 1232 10x + x2 = 0 + 1232 Combine like terms: 0 + 1232 = 1232 10x + x2 = 1232 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 = 1232 + 25 Reorder the terms: 25 + 10x + x2 = 1232 + 25 Combine like terms: 1232 + 25 = 1257 25 + 10x + x2 = 1257 Factor a perfect square on the left side: (x + 5)(x + 5) = 1257 Calculate the square root of the right side: 35.454195802 Break this problem into two subproblems by setting (x + 5) equal to 35.454195802 and -35.454195802.Subproblem 1
x + 5 = 35.454195802 Simplifying x + 5 = 35.454195802 Reorder the terms: 5 + x = 35.454195802 Solving 5 + x = 35.454195802 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 = 35.454195802 + -5 Combine like terms: 5 + -5 = 0 0 + x = 35.454195802 + -5 x = 35.454195802 + -5 Combine like terms: 35.454195802 + -5 = 30.454195802 x = 30.454195802 Simplifying x = 30.454195802Subproblem 2
x + 5 = -35.454195802 Simplifying x + 5 = -35.454195802 Reorder the terms: 5 + x = -35.454195802 Solving 5 + x = -35.454195802 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 = -35.454195802 + -5 Combine like terms: 5 + -5 = 0 0 + x = -35.454195802 + -5 x = -35.454195802 + -5 Combine like terms: -35.454195802 + -5 = -40.454195802 x = -40.454195802 Simplifying x = -40.454195802Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.454195802, -40.454195802}
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