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Simplifying X2 + 18X + -288 = 0 Reorder the terms: -288 + 18X + X2 = 0 Solving -288 + 18X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 18X + 288 + X2 = 0 + 288 Reorder the terms: -288 + 288 + 18X + X2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 18X + X2 = 0 + 288 18X + X2 = 0 + 288 Combine like terms: 0 + 288 = 288 18X + X2 = 288 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 = 288 + 81 Reorder the terms: 81 + 18X + X2 = 288 + 81 Combine like terms: 288 + 81 = 369 81 + 18X + X2 = 369 Factor a perfect square on the left side: (X + 9)(X + 9) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (X + 9) equal to 19.209372712 and -19.209372712.Subproblem 1
X + 9 = 19.209372712 Simplifying X + 9 = 19.209372712 Reorder the terms: 9 + X = 19.209372712 Solving 9 + X = 19.209372712 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 = 19.209372712 + -9 Combine like terms: 9 + -9 = 0 0 + X = 19.209372712 + -9 X = 19.209372712 + -9 Combine like terms: 19.209372712 + -9 = 10.209372712 X = 10.209372712 Simplifying X = 10.209372712Subproblem 2
X + 9 = -19.209372712 Simplifying X + 9 = -19.209372712 Reorder the terms: 9 + X = -19.209372712 Solving 9 + X = -19.209372712 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 = -19.209372712 + -9 Combine like terms: 9 + -9 = 0 0 + X = -19.209372712 + -9 X = -19.209372712 + -9 Combine like terms: -19.209372712 + -9 = -28.209372712 X = -28.209372712 Simplifying X = -28.209372712Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.209372712, -28.209372712}
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