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Simplifying X * X + 3X + -48 = 3498 Multiply X * X X2 + 3X + -48 = 3498 Reorder the terms: -48 + 3X + X2 = 3498 Solving -48 + 3X + X2 = 3498 Solving for variable 'X'. Reorder the terms: -48 + -3498 + 3X + X2 = 3498 + -3498 Combine like terms: -48 + -3498 = -3546 -3546 + 3X + X2 = 3498 + -3498 Combine like terms: 3498 + -3498 = 0 -3546 + 3X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '3546' to each side of the equation. -3546 + 3X + 3546 + X2 = 0 + 3546 Reorder the terms: -3546 + 3546 + 3X + X2 = 0 + 3546 Combine like terms: -3546 + 3546 = 0 0 + 3X + X2 = 0 + 3546 3X + X2 = 0 + 3546 Combine like terms: 0 + 3546 = 3546 3X + X2 = 3546 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = 3546 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 3546 + 2.25 Combine like terms: 3546 + 2.25 = 3548.25 2.25 + 3X + X2 = 3548.25 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 3548.25 Calculate the square root of the right side: 59.567188955 Break this problem into two subproblems by setting (X + 1.5) equal to 59.567188955 and -59.567188955.Subproblem 1
X + 1.5 = 59.567188955 Simplifying X + 1.5 = 59.567188955 Reorder the terms: 1.5 + X = 59.567188955 Solving 1.5 + X = 59.567188955 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 59.567188955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 59.567188955 + -1.5 X = 59.567188955 + -1.5 Combine like terms: 59.567188955 + -1.5 = 58.067188955 X = 58.067188955 Simplifying X = 58.067188955Subproblem 2
X + 1.5 = -59.567188955 Simplifying X + 1.5 = -59.567188955 Reorder the terms: 1.5 + X = -59.567188955 Solving 1.5 + X = -59.567188955 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -59.567188955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -59.567188955 + -1.5 X = -59.567188955 + -1.5 Combine like terms: -59.567188955 + -1.5 = -61.067188955 X = -61.067188955 Simplifying X = -61.067188955Solution
The solution to the problem is based on the solutions from the subproblems. X = {58.067188955, -61.067188955}
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