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Simplifying -4.9x2 + 30.5x + 8.1 = 0 Reorder the terms: 8.1 + 30.5x + -4.9x2 = 0 Solving 8.1 + 30.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -1.653061224 + -6.224489796x + x2 = 0 Move the constant term to the right: Add '1.653061224' to each side of the equation. -1.653061224 + -6.224489796x + 1.653061224 + x2 = 0 + 1.653061224 Reorder the terms: -1.653061224 + 1.653061224 + -6.224489796x + x2 = 0 + 1.653061224 Combine like terms: -1.653061224 + 1.653061224 = 0.000000000 0.000000000 + -6.224489796x + x2 = 0 + 1.653061224 -6.224489796x + x2 = 0 + 1.653061224 Combine like terms: 0 + 1.653061224 = 1.653061224 -6.224489796x + x2 = 1.653061224 The x term is -6.224489796x. Take half its coefficient (-3.112244898). Square it (9.686068305) and add it to both sides. Add '9.686068305' to each side of the equation. -6.224489796x + 9.686068305 + x2 = 1.653061224 + 9.686068305 Reorder the terms: 9.686068305 + -6.224489796x + x2 = 1.653061224 + 9.686068305 Combine like terms: 1.653061224 + 9.686068305 = 11.339129529 9.686068305 + -6.224489796x + x2 = 11.339129529 Factor a perfect square on the left side: (x + -3.112244898)(x + -3.112244898) = 11.339129529 Calculate the square root of the right side: 3.367362399 Break this problem into two subproblems by setting (x + -3.112244898) equal to 3.367362399 and -3.367362399.Subproblem 1
x + -3.112244898 = 3.367362399 Simplifying x + -3.112244898 = 3.367362399 Reorder the terms: -3.112244898 + x = 3.367362399 Solving -3.112244898 + x = 3.367362399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + x = 3.367362399 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + x = 3.367362399 + 3.112244898 x = 3.367362399 + 3.112244898 Combine like terms: 3.367362399 + 3.112244898 = 6.479607297 x = 6.479607297 Simplifying x = 6.479607297Subproblem 2
x + -3.112244898 = -3.367362399 Simplifying x + -3.112244898 = -3.367362399 Reorder the terms: -3.112244898 + x = -3.367362399 Solving -3.112244898 + x = -3.367362399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + x = -3.367362399 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + x = -3.367362399 + 3.112244898 x = -3.367362399 + 3.112244898 Combine like terms: -3.367362399 + 3.112244898 = -0.255117501 x = -0.255117501 Simplifying x = -0.255117501Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.479607297, -0.255117501}
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