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Simplifying 4x2 + -50x + 9 = 0 Reorder the terms: 9 + -50x + 4x2 = 0 Solving 9 + -50x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -12.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -12.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -12.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -12.5x + x2 = 0 + -2.25 -12.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -12.5x + x2 = -2.25 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -2.25 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -2.25 + 39.0625 Combine like terms: -2.25 + 39.0625 = 36.8125 39.0625 + -12.5x + x2 = 36.8125 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 36.8125 Calculate the square root of the right side: 6.06733055 Break this problem into two subproblems by setting (x + -6.25) equal to 6.06733055 and -6.06733055.Subproblem 1
x + -6.25 = 6.06733055 Simplifying x + -6.25 = 6.06733055 Reorder the terms: -6.25 + x = 6.06733055 Solving -6.25 + x = 6.06733055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 6.06733055 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.06733055 + 6.25 x = 6.06733055 + 6.25 Combine like terms: 6.06733055 + 6.25 = 12.31733055 x = 12.31733055 Simplifying x = 12.31733055Subproblem 2
x + -6.25 = -6.06733055 Simplifying x + -6.25 = -6.06733055 Reorder the terms: -6.25 + x = -6.06733055 Solving -6.25 + x = -6.06733055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -6.06733055 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.06733055 + 6.25 x = -6.06733055 + 6.25 Combine like terms: -6.06733055 + 6.25 = 0.18266945 x = 0.18266945 Simplifying x = 0.18266945Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.31733055, 0.18266945}
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