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Simplifying 8x2 + -8x + -3 = 0 Reorder the terms: -3 + -8x + 8x2 = 0 Solving -3 + -8x + 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'. -0.375 + -1x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1x + x2 = 0 + 0.375 -1x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1x + x2 = 0.375 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.375 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.375 + 0.25 Combine like terms: 0.375 + 0.25 = 0.625 0.25 + -1x + x2 = 0.625 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + -0.5) equal to 0.790569415 and -0.790569415.Subproblem 1
x + -0.5 = 0.790569415 Simplifying x + -0.5 = 0.790569415 Reorder the terms: -0.5 + x = 0.790569415 Solving -0.5 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.790569415 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.790569415 + 0.5 x = 0.790569415 + 0.5 Combine like terms: 0.790569415 + 0.5 = 1.290569415 x = 1.290569415 Simplifying x = 1.290569415Subproblem 2
x + -0.5 = -0.790569415 Simplifying x + -0.5 = -0.790569415 Reorder the terms: -0.5 + x = -0.790569415 Solving -0.5 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.790569415 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.790569415 + 0.5 x = -0.790569415 + 0.5 Combine like terms: -0.790569415 + 0.5 = -0.290569415 x = -0.290569415 Simplifying x = -0.290569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.290569415, -0.290569415}
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