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Simplifying 8x2 + 106x + -105 = 0 Reorder the terms: -105 + 106x + 8x2 = 0 Solving -105 + 106x + 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'. -13.125 + 13.25x + x2 = 0 Move the constant term to the right: Add '13.125' to each side of the equation. -13.125 + 13.25x + 13.125 + x2 = 0 + 13.125 Reorder the terms: -13.125 + 13.125 + 13.25x + x2 = 0 + 13.125 Combine like terms: -13.125 + 13.125 = 0.000 0.000 + 13.25x + x2 = 0 + 13.125 13.25x + x2 = 0 + 13.125 Combine like terms: 0 + 13.125 = 13.125 13.25x + x2 = 13.125 The x term is 13.25x. Take half its coefficient (6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. 13.25x + 43.890625 + x2 = 13.125 + 43.890625 Reorder the terms: 43.890625 + 13.25x + x2 = 13.125 + 43.890625 Combine like terms: 13.125 + 43.890625 = 57.015625 43.890625 + 13.25x + x2 = 57.015625 Factor a perfect square on the left side: (x + 6.625)(x + 6.625) = 57.015625 Calculate the square root of the right side: 7.550869155 Break this problem into two subproblems by setting (x + 6.625) equal to 7.550869155 and -7.550869155.Subproblem 1
x + 6.625 = 7.550869155 Simplifying x + 6.625 = 7.550869155 Reorder the terms: 6.625 + x = 7.550869155 Solving 6.625 + x = 7.550869155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.625' to each side of the equation. 6.625 + -6.625 + x = 7.550869155 + -6.625 Combine like terms: 6.625 + -6.625 = 0.000 0.000 + x = 7.550869155 + -6.625 x = 7.550869155 + -6.625 Combine like terms: 7.550869155 + -6.625 = 0.925869155 x = 0.925869155 Simplifying x = 0.925869155Subproblem 2
x + 6.625 = -7.550869155 Simplifying x + 6.625 = -7.550869155 Reorder the terms: 6.625 + x = -7.550869155 Solving 6.625 + x = -7.550869155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.625' to each side of the equation. 6.625 + -6.625 + x = -7.550869155 + -6.625 Combine like terms: 6.625 + -6.625 = 0.000 0.000 + x = -7.550869155 + -6.625 x = -7.550869155 + -6.625 Combine like terms: -7.550869155 + -6.625 = -14.175869155 x = -14.175869155 Simplifying x = -14.175869155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.925869155, -14.175869155}
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