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Simplifying x2 + 18x + -78 = 0 Reorder the terms: -78 + 18x + x2 = 0 Solving -78 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 18x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 18x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 18x + x2 = 0 + 78 18x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 18x + x2 = 78 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 = 78 + 81 Reorder the terms: 81 + 18x + x2 = 78 + 81 Combine like terms: 78 + 81 = 159 81 + 18x + x2 = 159 Factor a perfect square on the left side: (x + 9)(x + 9) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (x + 9) equal to 12.609520213 and -12.609520213.Subproblem 1
x + 9 = 12.609520213 Simplifying x + 9 = 12.609520213 Reorder the terms: 9 + x = 12.609520213 Solving 9 + x = 12.609520213 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 = 12.609520213 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.609520213 + -9 x = 12.609520213 + -9 Combine like terms: 12.609520213 + -9 = 3.609520213 x = 3.609520213 Simplifying x = 3.609520213Subproblem 2
x + 9 = -12.609520213 Simplifying x + 9 = -12.609520213 Reorder the terms: 9 + x = -12.609520213 Solving 9 + x = -12.609520213 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 = -12.609520213 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.609520213 + -9 x = -12.609520213 + -9 Combine like terms: -12.609520213 + -9 = -21.609520213 x = -21.609520213 Simplifying x = -21.609520213Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.609520213, -21.609520213}
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