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Simplifying 2x2 + 15x + 24 = 0 Reorder the terms: 24 + 15x + 2x2 = 0 Solving 24 + 15x + 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'. 12 + 7.5x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 7.5x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 7.5x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 7.5x + x2 = 0 + -12 7.5x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 7.5x + x2 = -12 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 = -12 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -12 + 14.0625 Combine like terms: -12 + 14.0625 = 2.0625 14.0625 + 7.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + 3.75) equal to 1.436140662 and -1.436140662.Subproblem 1
x + 3.75 = 1.436140662 Simplifying x + 3.75 = 1.436140662 Reorder the terms: 3.75 + x = 1.436140662 Solving 3.75 + x = 1.436140662 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 = 1.436140662 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 1.436140662 + -3.75 x = 1.436140662 + -3.75 Combine like terms: 1.436140662 + -3.75 = -2.313859338 x = -2.313859338 Simplifying x = -2.313859338Subproblem 2
x + 3.75 = -1.436140662 Simplifying x + 3.75 = -1.436140662 Reorder the terms: 3.75 + x = -1.436140662 Solving 3.75 + x = -1.436140662 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 = -1.436140662 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -1.436140662 + -3.75 x = -1.436140662 + -3.75 Combine like terms: -1.436140662 + -3.75 = -5.186140662 x = -5.186140662 Simplifying x = -5.186140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.313859338, -5.186140662}
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