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Simplifying x2 + 2x = 793 Reorder the terms: 2x + x2 = 793 Solving 2x + x2 = 793 Solving for variable 'x'. Reorder the terms: -793 + 2x + x2 = 793 + -793 Combine like terms: 793 + -793 = 0 -793 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '793' to each side of the equation. -793 + 2x + 793 + x2 = 0 + 793 Reorder the terms: -793 + 793 + 2x + x2 = 0 + 793 Combine like terms: -793 + 793 = 0 0 + 2x + x2 = 0 + 793 2x + x2 = 0 + 793 Combine like terms: 0 + 793 = 793 2x + x2 = 793 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 793 + 1 Reorder the terms: 1 + 2x + x2 = 793 + 1 Combine like terms: 793 + 1 = 794 1 + 2x + x2 = 794 Factor a perfect square on the left side: (x + 1)(x + 1) = 794 Calculate the square root of the right side: 28.178005607 Break this problem into two subproblems by setting (x + 1) equal to 28.178005607 and -28.178005607.Subproblem 1
x + 1 = 28.178005607 Simplifying x + 1 = 28.178005607 Reorder the terms: 1 + x = 28.178005607 Solving 1 + x = 28.178005607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 28.178005607 + -1 Combine like terms: 1 + -1 = 0 0 + x = 28.178005607 + -1 x = 28.178005607 + -1 Combine like terms: 28.178005607 + -1 = 27.178005607 x = 27.178005607 Simplifying x = 27.178005607Subproblem 2
x + 1 = -28.178005607 Simplifying x + 1 = -28.178005607 Reorder the terms: 1 + x = -28.178005607 Solving 1 + x = -28.178005607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -28.178005607 + -1 Combine like terms: 1 + -1 = 0 0 + x = -28.178005607 + -1 x = -28.178005607 + -1 Combine like terms: -28.178005607 + -1 = -29.178005607 x = -29.178005607 Simplifying x = -29.178005607Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.178005607, -29.178005607}
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