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Simplifying 8x2 + -56x + 40 = 1 Reorder the terms: 40 + -56x + 8x2 = 1 Solving 40 + -56x + 8x2 = 1 Solving for variable 'x'. Reorder the terms: 40 + -1 + -56x + 8x2 = 1 + -1 Combine like terms: 40 + -1 = 39 39 + -56x + 8x2 = 1 + -1 Combine like terms: 1 + -1 = 0 39 + -56x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.875 + -7x + x2 = 0 Move the constant term to the right: Add '-4.875' to each side of the equation. 4.875 + -7x + -4.875 + x2 = 0 + -4.875 Reorder the terms: 4.875 + -4.875 + -7x + x2 = 0 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + -7x + x2 = 0 + -4.875 -7x + x2 = 0 + -4.875 Combine like terms: 0 + -4.875 = -4.875 -7x + x2 = -4.875 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 = -4.875 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -4.875 + 12.25 Combine like terms: -4.875 + 12.25 = 7.375 12.25 + -7x + x2 = 7.375 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 7.375 Calculate the square root of the right side: 2.715695123 Break this problem into two subproblems by setting (x + -3.5) equal to 2.715695123 and -2.715695123.Subproblem 1
x + -3.5 = 2.715695123 Simplifying x + -3.5 = 2.715695123 Reorder the terms: -3.5 + x = 2.715695123 Solving -3.5 + x = 2.715695123 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 = 2.715695123 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.715695123 + 3.5 x = 2.715695123 + 3.5 Combine like terms: 2.715695123 + 3.5 = 6.215695123 x = 6.215695123 Simplifying x = 6.215695123Subproblem 2
x + -3.5 = -2.715695123 Simplifying x + -3.5 = -2.715695123 Reorder the terms: -3.5 + x = -2.715695123 Solving -3.5 + x = -2.715695123 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 = -2.715695123 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.715695123 + 3.5 x = -2.715695123 + 3.5 Combine like terms: -2.715695123 + 3.5 = 0.784304877 x = 0.784304877 Simplifying x = 0.784304877Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.215695123, 0.784304877}
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