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Simplifying 0 = -0.08x2 + 0.58x + 35 Reorder the terms: 0 = 35 + 0.58x + -0.08x2 Solving 0 = 35 + 0.58x + -0.08x2 Solving for variable 'x'. Combine like terms: 0 + -35 = -35 -35 + -0.58x + 0.08x2 = 35 + 0.58x + -0.08x2 + -35 + -0.58x + 0.08x2 Reorder the terms: -35 + -0.58x + 0.08x2 = 35 + -35 + 0.58x + -0.58x + -0.08x2 + 0.08x2 Combine like terms: 35 + -35 = 0 -35 + -0.58x + 0.08x2 = 0 + 0.58x + -0.58x + -0.08x2 + 0.08x2 -35 + -0.58x + 0.08x2 = 0.58x + -0.58x + -0.08x2 + 0.08x2 Combine like terms: 0.58x + -0.58x = 0.00 -35 + -0.58x + 0.08x2 = 0.00 + -0.08x2 + 0.08x2 -35 + -0.58x + 0.08x2 = -0.08x2 + 0.08x2 Combine like terms: -0.08x2 + 0.08x2 = 0.00 -35 + -0.58x + 0.08x2 = 0.00 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -437.5 + -7.25x + x2 = 0 Move the constant term to the right: Add '437.5' to each side of the equation. -437.5 + -7.25x + 437.5 + x2 = 0 + 437.5 Reorder the terms: -437.5 + 437.5 + -7.25x + x2 = 0 + 437.5 Combine like terms: -437.5 + 437.5 = 0.0 0.0 + -7.25x + x2 = 0 + 437.5 -7.25x + x2 = 0 + 437.5 Combine like terms: 0 + 437.5 = 437.5 -7.25x + x2 = 437.5 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 437.5 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 437.5 + 13.140625 Combine like terms: 437.5 + 13.140625 = 450.640625 13.140625 + -7.25x + x2 = 450.640625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 450.640625 Calculate the square root of the right side: 21.228297741 Break this problem into two subproblems by setting (x + -3.625) equal to 21.228297741 and -21.228297741.Subproblem 1
x + -3.625 = 21.228297741 Simplifying x + -3.625 = 21.228297741 Reorder the terms: -3.625 + x = 21.228297741 Solving -3.625 + x = 21.228297741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 21.228297741 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 21.228297741 + 3.625 x = 21.228297741 + 3.625 Combine like terms: 21.228297741 + 3.625 = 24.853297741 x = 24.853297741 Simplifying x = 24.853297741Subproblem 2
x + -3.625 = -21.228297741 Simplifying x + -3.625 = -21.228297741 Reorder the terms: -3.625 + x = -21.228297741 Solving -3.625 + x = -21.228297741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -21.228297741 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -21.228297741 + 3.625 x = -21.228297741 + 3.625 Combine like terms: -21.228297741 + 3.625 = -17.603297741 x = -17.603297741 Simplifying x = -17.603297741Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.853297741, -17.603297741}
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