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Simplifying X2 + 1X + -288 = 0 Reorder the terms: -288 + 1X + X2 = 0 Solving -288 + 1X + 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 + 1X + 288 + X2 = 0 + 288 Reorder the terms: -288 + 288 + 1X + X2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 1X + X2 = 0 + 288 1X + X2 = 0 + 288 Combine like terms: 0 + 288 = 288 1X + X2 = 288 The X term is 1X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. X + 0.25 + X2 = 288 + 0.25 Reorder the terms: 0.25 + X + X2 = 288 + 0.25 Combine like terms: 288 + 0.25 = 288.25 0.25 + X + X2 = 288.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (X + 0.5) equal to 16.977926846 and -16.977926846.Subproblem 1
X + 0.5 = 16.977926846 Simplifying X + 0.5 = 16.977926846 Reorder the terms: 0.5 + X = 16.977926846 Solving 0.5 + X = 16.977926846 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 16.977926846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 16.977926846 + -0.5 X = 16.977926846 + -0.5 Combine like terms: 16.977926846 + -0.5 = 16.477926846 X = 16.477926846 Simplifying X = 16.477926846Subproblem 2
X + 0.5 = -16.977926846 Simplifying X + 0.5 = -16.977926846 Reorder the terms: 0.5 + X = -16.977926846 Solving 0.5 + X = -16.977926846 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -16.977926846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -16.977926846 + -0.5 X = -16.977926846 + -0.5 Combine like terms: -16.977926846 + -0.5 = -17.477926846 X = -17.477926846 Simplifying X = -17.477926846Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.477926846, -17.477926846}
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