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Simplifying 2x2 + 29x + 85 = 0 Reorder the terms: 85 + 29x + 2x2 = 0 Solving 85 + 29x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 42.5 + 14.5x + x2 = 0 Move the constant term to the right: Add '-42.5' to each side of the equation. 42.5 + 14.5x + -42.5 + x2 = 0 + -42.5 Reorder the terms: 42.5 + -42.5 + 14.5x + x2 = 0 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + 14.5x + x2 = 0 + -42.5 14.5x + x2 = 0 + -42.5 Combine like terms: 0 + -42.5 = -42.5 14.5x + x2 = -42.5 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = -42.5 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = -42.5 + 52.5625 Combine like terms: -42.5 + 52.5625 = 10.0625 52.5625 + 14.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 7.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 7.25 = 3.172144385 Simplifying x + 7.25 = 3.172144385 Reorder the terms: 7.25 + x = 3.172144385 Solving 7.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 3.172144385 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 3.172144385 + -7.25 x = 3.172144385 + -7.25 Combine like terms: 3.172144385 + -7.25 = -4.077855615 x = -4.077855615 Simplifying x = -4.077855615Subproblem 2
x + 7.25 = -3.172144385 Simplifying x + 7.25 = -3.172144385 Reorder the terms: 7.25 + x = -3.172144385 Solving 7.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -3.172144385 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -3.172144385 + -7.25 x = -3.172144385 + -7.25 Combine like terms: -3.172144385 + -7.25 = -10.422144385 x = -10.422144385 Simplifying x = -10.422144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.077855615, -10.422144385}
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