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Simplifying 4x2 + 76x + -805 = 0 Reorder the terms: -805 + 76x + 4x2 = 0 Solving -805 + 76x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -201.25 + 19x + x2 = 0 Move the constant term to the right: Add '201.25' to each side of the equation. -201.25 + 19x + 201.25 + x2 = 0 + 201.25 Reorder the terms: -201.25 + 201.25 + 19x + x2 = 0 + 201.25 Combine like terms: -201.25 + 201.25 = 0.00 0.00 + 19x + x2 = 0 + 201.25 19x + x2 = 0 + 201.25 Combine like terms: 0 + 201.25 = 201.25 19x + x2 = 201.25 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 201.25 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 201.25 + 90.25 Combine like terms: 201.25 + 90.25 = 291.5 90.25 + 19x + x2 = 291.5 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 291.5 Calculate the square root of the right side: 17.073371079 Break this problem into two subproblems by setting (x + 9.5) equal to 17.073371079 and -17.073371079.Subproblem 1
x + 9.5 = 17.073371079 Simplifying x + 9.5 = 17.073371079 Reorder the terms: 9.5 + x = 17.073371079 Solving 9.5 + x = 17.073371079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 17.073371079 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 17.073371079 + -9.5 x = 17.073371079 + -9.5 Combine like terms: 17.073371079 + -9.5 = 7.573371079 x = 7.573371079 Simplifying x = 7.573371079Subproblem 2
x + 9.5 = -17.073371079 Simplifying x + 9.5 = -17.073371079 Reorder the terms: 9.5 + x = -17.073371079 Solving 9.5 + x = -17.073371079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -17.073371079 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -17.073371079 + -9.5 x = -17.073371079 + -9.5 Combine like terms: -17.073371079 + -9.5 = -26.573371079 x = -26.573371079 Simplifying x = -26.573371079Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.573371079, -26.573371079}
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