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Simplifying 8x2 + 41x + -140 = 0 Reorder the terms: -140 + 41x + 8x2 = 0 Solving -140 + 41x + 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'. -17.5 + 5.125x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 5.125x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 5.125x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 5.125x + x2 = 0 + 17.5 5.125x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 5.125x + x2 = 17.5 The x term is 5.125x. Take half its coefficient (2.5625). Square it (6.56640625) and add it to both sides. Add '6.56640625' to each side of the equation. 5.125x + 6.56640625 + x2 = 17.5 + 6.56640625 Reorder the terms: 6.56640625 + 5.125x + x2 = 17.5 + 6.56640625 Combine like terms: 17.5 + 6.56640625 = 24.06640625 6.56640625 + 5.125x + x2 = 24.06640625 Factor a perfect square on the left side: (x + 2.5625)(x + 2.5625) = 24.06640625 Calculate the square root of the right side: 4.905752363 Break this problem into two subproblems by setting (x + 2.5625) equal to 4.905752363 and -4.905752363.Subproblem 1
x + 2.5625 = 4.905752363 Simplifying x + 2.5625 = 4.905752363 Reorder the terms: 2.5625 + x = 4.905752363 Solving 2.5625 + x = 4.905752363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5625' to each side of the equation. 2.5625 + -2.5625 + x = 4.905752363 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = 4.905752363 + -2.5625 x = 4.905752363 + -2.5625 Combine like terms: 4.905752363 + -2.5625 = 2.343252363 x = 2.343252363 Simplifying x = 2.343252363Subproblem 2
x + 2.5625 = -4.905752363 Simplifying x + 2.5625 = -4.905752363 Reorder the terms: 2.5625 + x = -4.905752363 Solving 2.5625 + x = -4.905752363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5625' to each side of the equation. 2.5625 + -2.5625 + x = -4.905752363 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = -4.905752363 + -2.5625 x = -4.905752363 + -2.5625 Combine like terms: -4.905752363 + -2.5625 = -7.468252363 x = -7.468252363 Simplifying x = -7.468252363Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.343252363, -7.468252363}
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