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Simplifying X2 + 3X + -196 = 0 Reorder the terms: -196 + 3X + X2 = 0 Solving -196 + 3X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 3X + 196 + X2 = 0 + 196 Reorder the terms: -196 + 196 + 3X + X2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 3X + X2 = 0 + 196 3X + X2 = 0 + 196 Combine like terms: 0 + 196 = 196 3X + X2 = 196 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 = 196 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 196 + 2.25 Combine like terms: 196 + 2.25 = 198.25 2.25 + 3X + X2 = 198.25 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (X + 1.5) equal to 14.08012784 and -14.08012784.Subproblem 1
X + 1.5 = 14.08012784 Simplifying X + 1.5 = 14.08012784 Reorder the terms: 1.5 + X = 14.08012784 Solving 1.5 + X = 14.08012784 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 = 14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 14.08012784 + -1.5 X = 14.08012784 + -1.5 Combine like terms: 14.08012784 + -1.5 = 12.58012784 X = 12.58012784 Simplifying X = 12.58012784Subproblem 2
X + 1.5 = -14.08012784 Simplifying X + 1.5 = -14.08012784 Reorder the terms: 1.5 + X = -14.08012784 Solving 1.5 + X = -14.08012784 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 = -14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -14.08012784 + -1.5 X = -14.08012784 + -1.5 Combine like terms: -14.08012784 + -1.5 = -15.58012784 X = -15.58012784 Simplifying X = -15.58012784Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.58012784, -15.58012784}
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