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Simplifying 8x2 + -25x + -12 = 0 Reorder the terms: -12 + -25x + 8x2 = 0 Solving -12 + -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'. -1.5 + -3.125x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.125x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.125x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.125x + x2 = 0 + 1.5 -3.125x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.125x + x2 = 1.5 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 = 1.5 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 1.5 + 2.44140625 Combine like terms: 1.5 + 2.44140625 = 3.94140625 2.44140625 + -3.125x + x2 = 3.94140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 3.94140625 Calculate the square root of the right side: 1.985297522 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.985297522 and -1.985297522.Subproblem 1
x + -1.5625 = 1.985297522 Simplifying x + -1.5625 = 1.985297522 Reorder the terms: -1.5625 + x = 1.985297522 Solving -1.5625 + x = 1.985297522 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 = 1.985297522 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.985297522 + 1.5625 x = 1.985297522 + 1.5625 Combine like terms: 1.985297522 + 1.5625 = 3.547797522 x = 3.547797522 Simplifying x = 3.547797522Subproblem 2
x + -1.5625 = -1.985297522 Simplifying x + -1.5625 = -1.985297522 Reorder the terms: -1.5625 + x = -1.985297522 Solving -1.5625 + x = -1.985297522 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 = -1.985297522 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.985297522 + 1.5625 x = -1.985297522 + 1.5625 Combine like terms: -1.985297522 + 1.5625 = -0.422797522 x = -0.422797522 Simplifying x = -0.422797522Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.547797522, -0.422797522}
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