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Simplifying 8x2 + 9x + -24 = 0 Reorder the terms: -24 + 9x + 8x2 = 0 Solving -24 + 9x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3 + 1.125x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.125x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.125x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.125x + x2 = 0 + 3 1.125x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.125x + x2 = 3 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 3 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 3 + 0.31640625 Combine like terms: 3 + 0.31640625 = 3.31640625 0.31640625 + 1.125x + x2 = 3.31640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 3.31640625 Calculate the square root of the right side: 1.821100286 Break this problem into two subproblems by setting (x + 0.5625) equal to 1.821100286 and -1.821100286.Subproblem 1
x + 0.5625 = 1.821100286 Simplifying x + 0.5625 = 1.821100286 Reorder the terms: 0.5625 + x = 1.821100286 Solving 0.5625 + x = 1.821100286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 1.821100286 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.821100286 + -0.5625 x = 1.821100286 + -0.5625 Combine like terms: 1.821100286 + -0.5625 = 1.258600286 x = 1.258600286 Simplifying x = 1.258600286Subproblem 2
x + 0.5625 = -1.821100286 Simplifying x + 0.5625 = -1.821100286 Reorder the terms: 0.5625 + x = -1.821100286 Solving 0.5625 + x = -1.821100286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -1.821100286 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.821100286 + -0.5625 x = -1.821100286 + -0.5625 Combine like terms: -1.821100286 + -0.5625 = -2.383600286 x = -2.383600286 Simplifying x = -2.383600286Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.258600286, -2.383600286}
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