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Simplifying x2 + 18x = -4 Reorder the terms: 18x + x2 = -4 Solving 18x + x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 18x + x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 18x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 18x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 18x + x2 = 0 + -4 18x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 18x + x2 = -4 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 = -4 + 81 Reorder the terms: 81 + 18x + x2 = -4 + 81 Combine like terms: -4 + 81 = 77 81 + 18x + x2 = 77 Factor a perfect square on the left side: (x + 9)(x + 9) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 9) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 9 = 8.774964387 Simplifying x + 9 = 8.774964387 Reorder the terms: 9 + x = 8.774964387 Solving 9 + x = 8.774964387 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 = 8.774964387 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.774964387 + -9 x = 8.774964387 + -9 Combine like terms: 8.774964387 + -9 = -0.225035613 x = -0.225035613 Simplifying x = -0.225035613Subproblem 2
x + 9 = -8.774964387 Simplifying x + 9 = -8.774964387 Reorder the terms: 9 + x = -8.774964387 Solving 9 + x = -8.774964387 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 = -8.774964387 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.774964387 + -9 x = -8.774964387 + -9 Combine like terms: -8.774964387 + -9 = -17.774964387 x = -17.774964387 Simplifying x = -17.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.225035613, -17.774964387}
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