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Simplifying x2 + 20x + -77.8 = 0 Reorder the terms: -77.8 + 20x + x2 = 0 Solving -77.8 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '77.8' to each side of the equation. -77.8 + 20x + 77.8 + x2 = 0 + 77.8 Reorder the terms: -77.8 + 77.8 + 20x + x2 = 0 + 77.8 Combine like terms: -77.8 + 77.8 = 0.0 0.0 + 20x + x2 = 0 + 77.8 20x + x2 = 0 + 77.8 Combine like terms: 0 + 77.8 = 77.8 20x + x2 = 77.8 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 77.8 + 100 Reorder the terms: 100 + 20x + x2 = 77.8 + 100 Combine like terms: 77.8 + 100 = 177.8 100 + 20x + x2 = 177.8 Factor a perfect square on the left side: (x + 10)(x + 10) = 177.8 Calculate the square root of the right side: 13.334166641 Break this problem into two subproblems by setting (x + 10) equal to 13.334166641 and -13.334166641.Subproblem 1
x + 10 = 13.334166641 Simplifying x + 10 = 13.334166641 Reorder the terms: 10 + x = 13.334166641 Solving 10 + x = 13.334166641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 13.334166641 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.334166641 + -10 x = 13.334166641 + -10 Combine like terms: 13.334166641 + -10 = 3.334166641 x = 3.334166641 Simplifying x = 3.334166641Subproblem 2
x + 10 = -13.334166641 Simplifying x + 10 = -13.334166641 Reorder the terms: 10 + x = -13.334166641 Solving 10 + x = -13.334166641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -13.334166641 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.334166641 + -10 x = -13.334166641 + -10 Combine like terms: -13.334166641 + -10 = -23.334166641 x = -23.334166641 Simplifying x = -23.334166641Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.334166641, -23.334166641}
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