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Simplifying x2 + 18x + 10 = 0 Reorder the terms: 10 + 18x + x2 = 0 Solving 10 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 18x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 18x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 18x + x2 = 0 + -10 18x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 18x + x2 = -10 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 = -10 + 81 Reorder the terms: 81 + 18x + x2 = -10 + 81 Combine like terms: -10 + 81 = 71 81 + 18x + x2 = 71 Factor a perfect square on the left side: (x + 9)(x + 9) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 9) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 9 = 8.426149773 Simplifying x + 9 = 8.426149773 Reorder the terms: 9 + x = 8.426149773 Solving 9 + x = 8.426149773 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 = 8.426149773 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.426149773 + -9 x = 8.426149773 + -9 Combine like terms: 8.426149773 + -9 = -0.573850227 x = -0.573850227 Simplifying x = -0.573850227Subproblem 2
x + 9 = -8.426149773 Simplifying x + 9 = -8.426149773 Reorder the terms: 9 + x = -8.426149773 Solving 9 + x = -8.426149773 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 = -8.426149773 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.426149773 + -9 x = -8.426149773 + -9 Combine like terms: -8.426149773 + -9 = -17.426149773 x = -17.426149773 Simplifying x = -17.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.573850227, -17.426149773}
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