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Simplifying X2 + 15X + 6 = 0 Reorder the terms: 6 + 15X + X2 = 0 Solving 6 + 15X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 15X + -6 + X2 = 0 + -6 Reorder the terms: 6 + -6 + 15X + X2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 15X + X2 = 0 + -6 15X + X2 = 0 + -6 Combine like terms: 0 + -6 = -6 15X + X2 = -6 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 = -6 + 56.25 Reorder the terms: 56.25 + 15X + X2 = -6 + 56.25 Combine like terms: -6 + 56.25 = 50.25 56.25 + 15X + X2 = 50.25 Factor a perfect square on the left side: (X + 7.5)(X + 7.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (X + 7.5) equal to 7.088723439 and -7.088723439.Subproblem 1
X + 7.5 = 7.088723439 Simplifying X + 7.5 = 7.088723439 Reorder the terms: 7.5 + X = 7.088723439 Solving 7.5 + X = 7.088723439 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 = 7.088723439 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X = 7.088723439 + -7.5 X = 7.088723439 + -7.5 Combine like terms: 7.088723439 + -7.5 = -0.411276561 X = -0.411276561 Simplifying X = -0.411276561Subproblem 2
X + 7.5 = -7.088723439 Simplifying X + 7.5 = -7.088723439 Reorder the terms: 7.5 + X = -7.088723439 Solving 7.5 + X = -7.088723439 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 = -7.088723439 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X = -7.088723439 + -7.5 X = -7.088723439 + -7.5 Combine like terms: -7.088723439 + -7.5 = -14.588723439 X = -14.588723439 Simplifying X = -14.588723439Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.411276561, -14.588723439}
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