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Simplifying 1.6x2 + -19.6x + 60.025 = 0 Reorder the terms: 60.025 + -19.6x + 1.6x2 = 0 Solving 60.025 + -19.6x + 1.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. 37.515625 + -12.25x + x2 = 0 Move the constant term to the right: Add '-37.515625' to each side of the equation. 37.515625 + -12.25x + -37.515625 + x2 = 0 + -37.515625 Reorder the terms: 37.515625 + -37.515625 + -12.25x + x2 = 0 + -37.515625 Combine like terms: 37.515625 + -37.515625 = 0.000000 0.000000 + -12.25x + x2 = 0 + -37.515625 -12.25x + x2 = 0 + -37.515625 Combine like terms: 0 + -37.515625 = -37.515625 -12.25x + x2 = -37.515625 The x term is -12.25x. Take half its coefficient (-6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. -12.25x + 37.515625 + x2 = -37.515625 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = -37.515625 + 37.515625 Combine like terms: -37.515625 + 37.515625 = 0.000000 37.515625 + -12.25x + x2 = 0.000000 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 0.000000 Calculate the square root of the right side: 0.000000 Break this problem into two subproblems by setting (x + -6.125) equal to 0.000000 and 0.000000.Subproblem 1
x + -6.125 = 0.000000 Simplifying x + -6.125 = 0.000000 Reorder the terms: -6.125 + x = 0.000000 Solving -6.125 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 0.000000 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 0.000000 + 6.125 x = 0.000000 + 6.125 Combine like terms: 0.000000 + 6.125 = 6.125 x = 6.125 Simplifying x = 6.125Subproblem 2
x + -6.125 = 0.000000 Simplifying x + -6.125 = 0.000000 Reorder the terms: -6.125 + x = 0.000000 Solving -6.125 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 0.000000 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 0.000000 + 6.125 x = 0.000000 + 6.125 Combine like terms: 0.000000 + 6.125 = 6.125 x = 6.125 Simplifying x = 6.125Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.125, 6.125}
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