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Simplifying X2 + 15X + -43 = 0 Reorder the terms: -43 + 15X + X2 = 0 Solving -43 + 15X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 15X + 43 + X2 = 0 + 43 Reorder the terms: -43 + 43 + 15X + X2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 15X + X2 = 0 + 43 15X + X2 = 0 + 43 Combine like terms: 0 + 43 = 43 15X + X2 = 43 The X term is 15X. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15X + 56.25 + X2 = 43 + 56.25 Reorder the terms: 56.25 + 15X + X2 = 43 + 56.25 Combine like terms: 43 + 56.25 = 99.25 56.25 + 15X + X2 = 99.25 Factor a perfect square on the left side: (X + 7.5)(X + 7.5) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (X + 7.5) equal to 9.962429423 and -9.962429423.Subproblem 1
X + 7.5 = 9.962429423 Simplifying X + 7.5 = 9.962429423 Reorder the terms: 7.5 + X = 9.962429423 Solving 7.5 + X = 9.962429423 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + X = 9.962429423 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X = 9.962429423 + -7.5 X = 9.962429423 + -7.5 Combine like terms: 9.962429423 + -7.5 = 2.462429423 X = 2.462429423 Simplifying X = 2.462429423Subproblem 2
X + 7.5 = -9.962429423 Simplifying X + 7.5 = -9.962429423 Reorder the terms: 7.5 + X = -9.962429423 Solving 7.5 + X = -9.962429423 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + X = -9.962429423 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X = -9.962429423 + -7.5 X = -9.962429423 + -7.5 Combine like terms: -9.962429423 + -7.5 = -17.462429423 X = -17.462429423 Simplifying X = -17.462429423Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.462429423, -17.462429423}
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