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Simplifying x2 + -18x + 52 = 0 Reorder the terms: 52 + -18x + x2 = 0 Solving 52 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -18x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -18x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -18x + x2 = 0 + -52 -18x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -18x + x2 = -52 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -52 + 81 Reorder the terms: 81 + -18x + x2 = -52 + 81 Combine like terms: -52 + 81 = 29 81 + -18x + x2 = 29 Factor a perfect square on the left side: (x + -9)(x + -9) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -9) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -9 = 5.385164807 Simplifying x + -9 = 5.385164807 Reorder the terms: -9 + x = 5.385164807 Solving -9 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 5.385164807 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.385164807 + 9 x = 5.385164807 + 9 Combine like terms: 5.385164807 + 9 = 14.385164807 x = 14.385164807 Simplifying x = 14.385164807Subproblem 2
x + -9 = -5.385164807 Simplifying x + -9 = -5.385164807 Reorder the terms: -9 + x = -5.385164807 Solving -9 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -5.385164807 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.385164807 + 9 x = -5.385164807 + 9 Combine like terms: -5.385164807 + 9 = 3.614835193 x = 3.614835193 Simplifying x = 3.614835193Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.385164807, 3.614835193}
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