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Simplifying 8x2 + -10x + -11 = 0 Reorder the terms: -11 + -10x + 8x2 = 0 Solving -11 + -10x + 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'. -1.375 + -1.25x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -1.25x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -1.25x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -1.25x + x2 = 0 + 1.375 -1.25x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -1.25x + x2 = 1.375 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 1.375 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 1.375 + 0.390625 Combine like terms: 1.375 + 0.390625 = 1.765625 0.390625 + -1.25x + x2 = 1.765625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + -0.625) equal to 1.328768227 and -1.328768227.Subproblem 1
x + -0.625 = 1.328768227 Simplifying x + -0.625 = 1.328768227 Reorder the terms: -0.625 + x = 1.328768227 Solving -0.625 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.328768227 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.328768227 + 0.625 x = 1.328768227 + 0.625 Combine like terms: 1.328768227 + 0.625 = 1.953768227 x = 1.953768227 Simplifying x = 1.953768227Subproblem 2
x + -0.625 = -1.328768227 Simplifying x + -0.625 = -1.328768227 Reorder the terms: -0.625 + x = -1.328768227 Solving -0.625 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.328768227 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.328768227 + 0.625 x = -1.328768227 + 0.625 Combine like terms: -1.328768227 + 0.625 = -0.703768227 x = -0.703768227 Simplifying x = -0.703768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.953768227, -0.703768227}
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