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Simplifying x2 + 18x + 64 = 0 Reorder the terms: 64 + 18x + x2 = 0 Solving 64 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 18x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 18x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 18x + x2 = 0 + -64 18x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 18x + x2 = -64 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 = -64 + 81 Reorder the terms: 81 + 18x + x2 = -64 + 81 Combine like terms: -64 + 81 = 17 81 + 18x + x2 = 17 Factor a perfect square on the left side: (x + 9)(x + 9) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 9) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 9 = 4.123105626 Simplifying x + 9 = 4.123105626 Reorder the terms: 9 + x = 4.123105626 Solving 9 + x = 4.123105626 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 = 4.123105626 + -9 Combine like terms: 9 + -9 = 0 0 + x = 4.123105626 + -9 x = 4.123105626 + -9 Combine like terms: 4.123105626 + -9 = -4.876894374 x = -4.876894374 Simplifying x = -4.876894374Subproblem 2
x + 9 = -4.123105626 Simplifying x + 9 = -4.123105626 Reorder the terms: 9 + x = -4.123105626 Solving 9 + x = -4.123105626 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 = -4.123105626 + -9 Combine like terms: 9 + -9 = 0 0 + x = -4.123105626 + -9 x = -4.123105626 + -9 Combine like terms: -4.123105626 + -9 = -13.123105626 x = -13.123105626 Simplifying x = -13.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.876894374, -13.123105626}
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