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Simplifying 2x2 + -80x + -273 = 0 Reorder the terms: -273 + -80x + 2x2 = 0 Solving -273 + -80x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -136.5 + -40x + x2 = 0 Move the constant term to the right: Add '136.5' to each side of the equation. -136.5 + -40x + 136.5 + x2 = 0 + 136.5 Reorder the terms: -136.5 + 136.5 + -40x + x2 = 0 + 136.5 Combine like terms: -136.5 + 136.5 = 0.0 0.0 + -40x + x2 = 0 + 136.5 -40x + x2 = 0 + 136.5 Combine like terms: 0 + 136.5 = 136.5 -40x + x2 = 136.5 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 136.5 + 400 Reorder the terms: 400 + -40x + x2 = 136.5 + 400 Combine like terms: 136.5 + 400 = 536.5 400 + -40x + x2 = 536.5 Factor a perfect square on the left side: (x + -20)(x + -20) = 536.5 Calculate the square root of the right side: 23.162469644 Break this problem into two subproblems by setting (x + -20) equal to 23.162469644 and -23.162469644.Subproblem 1
x + -20 = 23.162469644 Simplifying x + -20 = 23.162469644 Reorder the terms: -20 + x = 23.162469644 Solving -20 + x = 23.162469644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 23.162469644 + 20 Combine like terms: -20 + 20 = 0 0 + x = 23.162469644 + 20 x = 23.162469644 + 20 Combine like terms: 23.162469644 + 20 = 43.162469644 x = 43.162469644 Simplifying x = 43.162469644Subproblem 2
x + -20 = -23.162469644 Simplifying x + -20 = -23.162469644 Reorder the terms: -20 + x = -23.162469644 Solving -20 + x = -23.162469644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -23.162469644 + 20 Combine like terms: -20 + 20 = 0 0 + x = -23.162469644 + 20 x = -23.162469644 + 20 Combine like terms: -23.162469644 + 20 = -3.162469644 x = -3.162469644 Simplifying x = -3.162469644Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.162469644, -3.162469644}
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