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Simplifying 2x2 + 9x + -24 = 0 Reorder the terms: -24 + 9x + 2x2 = 0 Solving -24 + 9x + 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 + 4.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 4.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 4.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 4.5x + x2 = 0 + 12 4.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 4.5x + x2 = 12 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 12 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 12 + 5.0625 Combine like terms: 12 + 5.0625 = 17.0625 5.0625 + 4.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + 2.25) equal to 4.13067791 and -4.13067791.Subproblem 1
x + 2.25 = 4.13067791 Simplifying x + 2.25 = 4.13067791 Reorder the terms: 2.25 + x = 4.13067791 Solving 2.25 + x = 4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.13067791 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.13067791 + -2.25 x = 4.13067791 + -2.25 Combine like terms: 4.13067791 + -2.25 = 1.88067791 x = 1.88067791 Simplifying x = 1.88067791Subproblem 2
x + 2.25 = -4.13067791 Simplifying x + 2.25 = -4.13067791 Reorder the terms: 2.25 + x = -4.13067791 Solving 2.25 + x = -4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.13067791 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.13067791 + -2.25 x = -4.13067791 + -2.25 Combine like terms: -4.13067791 + -2.25 = -6.38067791 x = -6.38067791 Simplifying x = -6.38067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.88067791, -6.38067791}
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