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Simplifying 8x2 + -56x + -3 = 0 Reorder the terms: -3 + -56x + 8x2 = 0 Solving -3 + -56x + 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 + -7x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -7x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -7x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -7x + x2 = 0 + 0.375 -7x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -7x + x2 = 0.375 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 0.375 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 0.375 + 12.25 Combine like terms: 0.375 + 12.25 = 12.625 12.25 + -7x + x2 = 12.625 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 12.625 Calculate the square root of the right side: 3.553167601 Break this problem into two subproblems by setting (x + -3.5) equal to 3.553167601 and -3.553167601.Subproblem 1
x + -3.5 = 3.553167601 Simplifying x + -3.5 = 3.553167601 Reorder the terms: -3.5 + x = 3.553167601 Solving -3.5 + x = 3.553167601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.553167601 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.553167601 + 3.5 x = 3.553167601 + 3.5 Combine like terms: 3.553167601 + 3.5 = 7.053167601 x = 7.053167601 Simplifying x = 7.053167601Subproblem 2
x + -3.5 = -3.553167601 Simplifying x + -3.5 = -3.553167601 Reorder the terms: -3.5 + x = -3.553167601 Solving -3.5 + x = -3.553167601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.553167601 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.553167601 + 3.5 x = -3.553167601 + 3.5 Combine like terms: -3.553167601 + 3.5 = -0.053167601 x = -0.053167601 Simplifying x = -0.053167601Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.053167601, -0.053167601}
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