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Simplifying 16x2 + -224.98x + -250 = 0 Reorder the terms: -250 + -224.98x + 16x2 = 0 Solving -250 + -224.98x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -15.625 + -14.06125x + x2 = 0 Move the constant term to the right: Add '15.625' to each side of the equation. -15.625 + -14.06125x + 15.625 + x2 = 0 + 15.625 Reorder the terms: -15.625 + 15.625 + -14.06125x + x2 = 0 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + -14.06125x + x2 = 0 + 15.625 -14.06125x + x2 = 0 + 15.625 Combine like terms: 0 + 15.625 = 15.625 -14.06125x + x2 = 15.625 The x term is -14.06125x. Take half its coefficient (-7.030625). Square it (49.42968789) and add it to both sides. Add '49.42968789' to each side of the equation. -14.06125x + 49.42968789 + x2 = 15.625 + 49.42968789 Reorder the terms: 49.42968789 + -14.06125x + x2 = 15.625 + 49.42968789 Combine like terms: 15.625 + 49.42968789 = 65.05468789 49.42968789 + -14.06125x + x2 = 65.05468789 Factor a perfect square on the left side: (x + -7.030625)(x + -7.030625) = 65.05468789 Calculate the square root of the right side: 8.065648634 Break this problem into two subproblems by setting (x + -7.030625) equal to 8.065648634 and -8.065648634.Subproblem 1
x + -7.030625 = 8.065648634 Simplifying x + -7.030625 = 8.065648634 Reorder the terms: -7.030625 + x = 8.065648634 Solving -7.030625 + x = 8.065648634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.030625' to each side of the equation. -7.030625 + 7.030625 + x = 8.065648634 + 7.030625 Combine like terms: -7.030625 + 7.030625 = 0.000000 0.000000 + x = 8.065648634 + 7.030625 x = 8.065648634 + 7.030625 Combine like terms: 8.065648634 + 7.030625 = 15.096273634 x = 15.096273634 Simplifying x = 15.096273634Subproblem 2
x + -7.030625 = -8.065648634 Simplifying x + -7.030625 = -8.065648634 Reorder the terms: -7.030625 + x = -8.065648634 Solving -7.030625 + x = -8.065648634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.030625' to each side of the equation. -7.030625 + 7.030625 + x = -8.065648634 + 7.030625 Combine like terms: -7.030625 + 7.030625 = 0.000000 0.000000 + x = -8.065648634 + 7.030625 x = -8.065648634 + 7.030625 Combine like terms: -8.065648634 + 7.030625 = -1.035023634 x = -1.035023634 Simplifying x = -1.035023634Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.096273634, -1.035023634}
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