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Simplifying 4x2 + 30x + -105 = 0 Reorder the terms: -105 + 30x + 4x2 = 0 Solving -105 + 30x + 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'. -26.25 + 7.5x + x2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + 7.5x + 26.25 + x2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + 7.5x + x2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + 7.5x + x2 = 0 + 26.25 7.5x + x2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 7.5x + x2 = 26.25 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 26.25 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 26.25 + 14.0625 Combine like terms: 26.25 + 14.0625 = 40.3125 14.0625 + 7.5x + x2 = 40.3125 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 40.3125 Calculate the square root of the right side: 6.34921255 Break this problem into two subproblems by setting (x + 3.75) equal to 6.34921255 and -6.34921255.Subproblem 1
x + 3.75 = 6.34921255 Simplifying x + 3.75 = 6.34921255 Reorder the terms: 3.75 + x = 6.34921255 Solving 3.75 + x = 6.34921255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 6.34921255 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 6.34921255 + -3.75 x = 6.34921255 + -3.75 Combine like terms: 6.34921255 + -3.75 = 2.59921255 x = 2.59921255 Simplifying x = 2.59921255Subproblem 2
x + 3.75 = -6.34921255 Simplifying x + 3.75 = -6.34921255 Reorder the terms: 3.75 + x = -6.34921255 Solving 3.75 + x = -6.34921255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -6.34921255 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -6.34921255 + -3.75 x = -6.34921255 + -3.75 Combine like terms: -6.34921255 + -3.75 = -10.09921255 x = -10.09921255 Simplifying x = -10.09921255Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.59921255, -10.09921255}
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