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Simplifying 8x2 + -25x + -24 = 0 Reorder the terms: -24 + -25x + 8x2 = 0 Solving -24 + -25x + 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 + -3.125x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.125x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -3.125x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.125x + x2 = 0 + 3 -3.125x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.125x + x2 = 3 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 3 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 3 + 2.44140625 Combine like terms: 3 + 2.44140625 = 5.44140625 2.44140625 + -3.125x + x2 = 5.44140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 5.44140625 Calculate the square root of the right side: 2.332682201 Break this problem into two subproblems by setting (x + -1.5625) equal to 2.332682201 and -2.332682201.Subproblem 1
x + -1.5625 = 2.332682201 Simplifying x + -1.5625 = 2.332682201 Reorder the terms: -1.5625 + x = 2.332682201 Solving -1.5625 + x = 2.332682201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 2.332682201 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 2.332682201 + 1.5625 x = 2.332682201 + 1.5625 Combine like terms: 2.332682201 + 1.5625 = 3.895182201 x = 3.895182201 Simplifying x = 3.895182201Subproblem 2
x + -1.5625 = -2.332682201 Simplifying x + -1.5625 = -2.332682201 Reorder the terms: -1.5625 + x = -2.332682201 Solving -1.5625 + x = -2.332682201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -2.332682201 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -2.332682201 + 1.5625 x = -2.332682201 + 1.5625 Combine like terms: -2.332682201 + 1.5625 = -0.770182201 x = -0.770182201 Simplifying x = -0.770182201Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.895182201, -0.770182201}
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