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Simplifying 2x2 + -5x + -105 = 0 Reorder the terms: -105 + -5x + 2x2 = 0 Solving -105 + -5x + 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'. -52.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '52.5' to each side of the equation. -52.5 + -2.5x + 52.5 + x2 = 0 + 52.5 Reorder the terms: -52.5 + 52.5 + -2.5x + x2 = 0 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + -2.5x + x2 = 0 + 52.5 -2.5x + x2 = 0 + 52.5 Combine like terms: 0 + 52.5 = 52.5 -2.5x + x2 = 52.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 52.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 52.5 + 1.5625 Combine like terms: 52.5 + 1.5625 = 54.0625 1.5625 + -2.5x + x2 = 54.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 54.0625 Calculate the square root of the right side: 7.352720585 Break this problem into two subproblems by setting (x + -1.25) equal to 7.352720585 and -7.352720585.Subproblem 1
x + -1.25 = 7.352720585 Simplifying x + -1.25 = 7.352720585 Reorder the terms: -1.25 + x = 7.352720585 Solving -1.25 + x = 7.352720585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 7.352720585 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 7.352720585 + 1.25 x = 7.352720585 + 1.25 Combine like terms: 7.352720585 + 1.25 = 8.602720585 x = 8.602720585 Simplifying x = 8.602720585Subproblem 2
x + -1.25 = -7.352720585 Simplifying x + -1.25 = -7.352720585 Reorder the terms: -1.25 + x = -7.352720585 Solving -1.25 + x = -7.352720585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -7.352720585 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -7.352720585 + 1.25 x = -7.352720585 + 1.25 Combine like terms: -7.352720585 + 1.25 = -6.102720585 x = -6.102720585 Simplifying x = -6.102720585Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.602720585, -6.102720585}
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