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Simplifying 8x2 + -99x + 235 = 0 Reorder the terms: 235 + -99x + 8x2 = 0 Solving 235 + -99x + 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'. 29.375 + -12.375x + x2 = 0 Move the constant term to the right: Add '-29.375' to each side of the equation. 29.375 + -12.375x + -29.375 + x2 = 0 + -29.375 Reorder the terms: 29.375 + -29.375 + -12.375x + x2 = 0 + -29.375 Combine like terms: 29.375 + -29.375 = 0.000 0.000 + -12.375x + x2 = 0 + -29.375 -12.375x + x2 = 0 + -29.375 Combine like terms: 0 + -29.375 = -29.375 -12.375x + x2 = -29.375 The x term is -12.375x. Take half its coefficient (-6.1875). Square it (38.28515625) and add it to both sides. Add '38.28515625' to each side of the equation. -12.375x + 38.28515625 + x2 = -29.375 + 38.28515625 Reorder the terms: 38.28515625 + -12.375x + x2 = -29.375 + 38.28515625 Combine like terms: -29.375 + 38.28515625 = 8.91015625 38.28515625 + -12.375x + x2 = 8.91015625 Factor a perfect square on the left side: (x + -6.1875)(x + -6.1875) = 8.91015625 Calculate the square root of the right side: 2.984988484 Break this problem into two subproblems by setting (x + -6.1875) equal to 2.984988484 and -2.984988484.Subproblem 1
x + -6.1875 = 2.984988484 Simplifying x + -6.1875 = 2.984988484 Reorder the terms: -6.1875 + x = 2.984988484 Solving -6.1875 + x = 2.984988484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.1875' to each side of the equation. -6.1875 + 6.1875 + x = 2.984988484 + 6.1875 Combine like terms: -6.1875 + 6.1875 = 0.0000 0.0000 + x = 2.984988484 + 6.1875 x = 2.984988484 + 6.1875 Combine like terms: 2.984988484 + 6.1875 = 9.172488484 x = 9.172488484 Simplifying x = 9.172488484Subproblem 2
x + -6.1875 = -2.984988484 Simplifying x + -6.1875 = -2.984988484 Reorder the terms: -6.1875 + x = -2.984988484 Solving -6.1875 + x = -2.984988484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.1875' to each side of the equation. -6.1875 + 6.1875 + x = -2.984988484 + 6.1875 Combine like terms: -6.1875 + 6.1875 = 0.0000 0.0000 + x = -2.984988484 + 6.1875 x = -2.984988484 + 6.1875 Combine like terms: -2.984988484 + 6.1875 = 3.202511516 x = 3.202511516 Simplifying x = 3.202511516Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.172488484, 3.202511516}
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