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Simplifying 1.5x2 + 6x + -8087 = 0 Reorder the terms: -8087 + 6x + 1.5x2 = 0 Solving -8087 + 6x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -5391.333333 + 4x + x2 = 0 Move the constant term to the right: Add '5391.333333' to each side of the equation. -5391.333333 + 4x + 5391.333333 + x2 = 0 + 5391.333333 Reorder the terms: -5391.333333 + 5391.333333 + 4x + x2 = 0 + 5391.333333 Combine like terms: -5391.333333 + 5391.333333 = 0.000000 0.000000 + 4x + x2 = 0 + 5391.333333 4x + x2 = 0 + 5391.333333 Combine like terms: 0 + 5391.333333 = 5391.333333 4x + x2 = 5391.333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 5391.333333 + 4 Reorder the terms: 4 + 4x + x2 = 5391.333333 + 4 Combine like terms: 5391.333333 + 4 = 5395.333333 4 + 4x + x2 = 5395.333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 5395.333333 Calculate the square root of the right side: 73.452932773 Break this problem into two subproblems by setting (x + 2) equal to 73.452932773 and -73.452932773.Subproblem 1
x + 2 = 73.452932773 Simplifying x + 2 = 73.452932773 Reorder the terms: 2 + x = 73.452932773 Solving 2 + x = 73.452932773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 73.452932773 + -2 Combine like terms: 2 + -2 = 0 0 + x = 73.452932773 + -2 x = 73.452932773 + -2 Combine like terms: 73.452932773 + -2 = 71.452932773 x = 71.452932773 Simplifying x = 71.452932773Subproblem 2
x + 2 = -73.452932773 Simplifying x + 2 = -73.452932773 Reorder the terms: 2 + x = -73.452932773 Solving 2 + x = -73.452932773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -73.452932773 + -2 Combine like terms: 2 + -2 = 0 0 + x = -73.452932773 + -2 x = -73.452932773 + -2 Combine like terms: -73.452932773 + -2 = -75.452932773 x = -75.452932773 Simplifying x = -75.452932773Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.452932773, -75.452932773}
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