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Simplifying -0.096x2 + 4.8x + 20 = 0 Reorder the terms: 20 + 4.8x + -0.096x2 = 0 Solving 20 + 4.8x + -0.096x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.096 the coefficient of the squared term: Divide each side by '-0.096'. -208.3333333 + -50x + x2 = 0 Move the constant term to the right: Add '208.3333333' to each side of the equation. -208.3333333 + -50x + 208.3333333 + x2 = 0 + 208.3333333 Reorder the terms: -208.3333333 + 208.3333333 + -50x + x2 = 0 + 208.3333333 Combine like terms: -208.3333333 + 208.3333333 = 0.0000000 0.0000000 + -50x + x2 = 0 + 208.3333333 -50x + x2 = 0 + 208.3333333 Combine like terms: 0 + 208.3333333 = 208.3333333 -50x + x2 = 208.3333333 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 208.3333333 + 625 Reorder the terms: 625 + -50x + x2 = 208.3333333 + 625 Combine like terms: 208.3333333 + 625 = 833.3333333 625 + -50x + x2 = 833.3333333 Factor a perfect square on the left side: (x + -25)(x + -25) = 833.3333333 Calculate the square root of the right side: 28.867513459 Break this problem into two subproblems by setting (x + -25) equal to 28.867513459 and -28.867513459.Subproblem 1
x + -25 = 28.867513459 Simplifying x + -25 = 28.867513459 Reorder the terms: -25 + x = 28.867513459 Solving -25 + x = 28.867513459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 28.867513459 + 25 Combine like terms: -25 + 25 = 0 0 + x = 28.867513459 + 25 x = 28.867513459 + 25 Combine like terms: 28.867513459 + 25 = 53.867513459 x = 53.867513459 Simplifying x = 53.867513459Subproblem 2
x + -25 = -28.867513459 Simplifying x + -25 = -28.867513459 Reorder the terms: -25 + x = -28.867513459 Solving -25 + x = -28.867513459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -28.867513459 + 25 Combine like terms: -25 + 25 = 0 0 + x = -28.867513459 + 25 x = -28.867513459 + 25 Combine like terms: -28.867513459 + 25 = -3.867513459 x = -3.867513459 Simplifying x = -3.867513459Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.867513459, -3.867513459}
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