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Simplifying 8x2 + 67x + -334 = 0 Reorder the terms: -334 + 67x + 8x2 = 0 Solving -334 + 67x + 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'. -41.75 + 8.375x + x2 = 0 Move the constant term to the right: Add '41.75' to each side of the equation. -41.75 + 8.375x + 41.75 + x2 = 0 + 41.75 Reorder the terms: -41.75 + 41.75 + 8.375x + x2 = 0 + 41.75 Combine like terms: -41.75 + 41.75 = 0.00 0.00 + 8.375x + x2 = 0 + 41.75 8.375x + x2 = 0 + 41.75 Combine like terms: 0 + 41.75 = 41.75 8.375x + x2 = 41.75 The x term is 8.375x. Take half its coefficient (4.1875). Square it (17.53515625) and add it to both sides. Add '17.53515625' to each side of the equation. 8.375x + 17.53515625 + x2 = 41.75 + 17.53515625 Reorder the terms: 17.53515625 + 8.375x + x2 = 41.75 + 17.53515625 Combine like terms: 41.75 + 17.53515625 = 59.28515625 17.53515625 + 8.375x + x2 = 59.28515625 Factor a perfect square on the left side: (x + 4.1875)(x + 4.1875) = 59.28515625 Calculate the square root of the right side: 7.699685464 Break this problem into two subproblems by setting (x + 4.1875) equal to 7.699685464 and -7.699685464.Subproblem 1
x + 4.1875 = 7.699685464 Simplifying x + 4.1875 = 7.699685464 Reorder the terms: 4.1875 + x = 7.699685464 Solving 4.1875 + x = 7.699685464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1875' to each side of the equation. 4.1875 + -4.1875 + x = 7.699685464 + -4.1875 Combine like terms: 4.1875 + -4.1875 = 0.0000 0.0000 + x = 7.699685464 + -4.1875 x = 7.699685464 + -4.1875 Combine like terms: 7.699685464 + -4.1875 = 3.512185464 x = 3.512185464 Simplifying x = 3.512185464Subproblem 2
x + 4.1875 = -7.699685464 Simplifying x + 4.1875 = -7.699685464 Reorder the terms: 4.1875 + x = -7.699685464 Solving 4.1875 + x = -7.699685464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1875' to each side of the equation. 4.1875 + -4.1875 + x = -7.699685464 + -4.1875 Combine like terms: 4.1875 + -4.1875 = 0.0000 0.0000 + x = -7.699685464 + -4.1875 x = -7.699685464 + -4.1875 Combine like terms: -7.699685464 + -4.1875 = -11.887185464 x = -11.887185464 Simplifying x = -11.887185464Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.512185464, -11.887185464}
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