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Simplifying x2 + -18x + 55 = 0 Reorder the terms: 55 + -18x + x2 = 0 Solving 55 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -18x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -18x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -18x + x2 = 0 + -55 -18x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -18x + x2 = -55 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 = -55 + 81 Reorder the terms: 81 + -18x + x2 = -55 + 81 Combine like terms: -55 + 81 = 26 81 + -18x + x2 = 26 Factor a perfect square on the left side: (x + -9)(x + -9) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -9) equal to 5.099019514 and -5.099019514.Subproblem 1
x + -9 = 5.099019514 Simplifying x + -9 = 5.099019514 Reorder the terms: -9 + x = 5.099019514 Solving -9 + x = 5.099019514 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 = 5.099019514 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.099019514 + 9 x = 5.099019514 + 9 Combine like terms: 5.099019514 + 9 = 14.099019514 x = 14.099019514 Simplifying x = 14.099019514Subproblem 2
x + -9 = -5.099019514 Simplifying x + -9 = -5.099019514 Reorder the terms: -9 + x = -5.099019514 Solving -9 + x = -5.099019514 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 = -5.099019514 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.099019514 + 9 x = -5.099019514 + 9 Combine like terms: -5.099019514 + 9 = 3.900980486 x = 3.900980486 Simplifying x = 3.900980486Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.099019514, 3.900980486}
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