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Simplifying 2x2 + 6x = 95 Reorder the terms: 6x + 2x2 = 95 Solving 6x + 2x2 = 95 Solving for variable 'x'. Reorder the terms: -95 + 6x + 2x2 = 95 + -95 Combine like terms: 95 + -95 = 0 -95 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -47.5 + 3x + x2 = 0 Move the constant term to the right: Add '47.5' to each side of the equation. -47.5 + 3x + 47.5 + x2 = 0 + 47.5 Reorder the terms: -47.5 + 47.5 + 3x + x2 = 0 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + 3x + x2 = 0 + 47.5 3x + x2 = 0 + 47.5 Combine like terms: 0 + 47.5 = 47.5 3x + x2 = 47.5 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 = 47.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 47.5 + 2.25 Combine like terms: 47.5 + 2.25 = 49.75 2.25 + 3x + x2 = 49.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 49.75 Calculate the square root of the right side: 7.05336799 Break this problem into two subproblems by setting (x + 1.5) equal to 7.05336799 and -7.05336799.Subproblem 1
x + 1.5 = 7.05336799 Simplifying x + 1.5 = 7.05336799 Reorder the terms: 1.5 + x = 7.05336799 Solving 1.5 + x = 7.05336799 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 = 7.05336799 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.05336799 + -1.5 x = 7.05336799 + -1.5 Combine like terms: 7.05336799 + -1.5 = 5.55336799 x = 5.55336799 Simplifying x = 5.55336799Subproblem 2
x + 1.5 = -7.05336799 Simplifying x + 1.5 = -7.05336799 Reorder the terms: 1.5 + x = -7.05336799 Solving 1.5 + x = -7.05336799 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 = -7.05336799 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.05336799 + -1.5 x = -7.05336799 + -1.5 Combine like terms: -7.05336799 + -1.5 = -8.55336799 x = -8.55336799 Simplifying x = -8.55336799Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.55336799, -8.55336799}
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