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Simplifying x2 + 18x = -79 Reorder the terms: 18x + x2 = -79 Solving 18x + x2 = -79 Solving for variable 'x'. Reorder the terms: 79 + 18x + x2 = -79 + 79 Combine like terms: -79 + 79 = 0 79 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-79' to each side of the equation. 79 + 18x + -79 + x2 = 0 + -79 Reorder the terms: 79 + -79 + 18x + x2 = 0 + -79 Combine like terms: 79 + -79 = 0 0 + 18x + x2 = 0 + -79 18x + x2 = 0 + -79 Combine like terms: 0 + -79 = -79 18x + x2 = -79 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 = -79 + 81 Reorder the terms: 81 + 18x + x2 = -79 + 81 Combine like terms: -79 + 81 = 2 81 + 18x + x2 = 2 Factor a perfect square on the left side: (x + 9)(x + 9) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 9) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 9 = 1.414213562 Simplifying x + 9 = 1.414213562 Reorder the terms: 9 + x = 1.414213562 Solving 9 + x = 1.414213562 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 = 1.414213562 + -9 Combine like terms: 9 + -9 = 0 0 + x = 1.414213562 + -9 x = 1.414213562 + -9 Combine like terms: 1.414213562 + -9 = -7.585786438 x = -7.585786438 Simplifying x = -7.585786438Subproblem 2
x + 9 = -1.414213562 Simplifying x + 9 = -1.414213562 Reorder the terms: 9 + x = -1.414213562 Solving 9 + x = -1.414213562 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 = -1.414213562 + -9 Combine like terms: 9 + -9 = 0 0 + x = -1.414213562 + -9 x = -1.414213562 + -9 Combine like terms: -1.414213562 + -9 = -10.414213562 x = -10.414213562 Simplifying x = -10.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.585786438, -10.414213562}
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