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Simplifying 2x2 + -55x + -800 = 0 Reorder the terms: -800 + -55x + 2x2 = 0 Solving -800 + -55x + 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'. -400 + -27.5x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -27.5x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -27.5x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -27.5x + x2 = 0 + 400 -27.5x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -27.5x + x2 = 400 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = 400 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = 400 + 189.0625 Combine like terms: 400 + 189.0625 = 589.0625 189.0625 + -27.5x + x2 = 589.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 589.0625 Calculate the square root of the right side: 24.270609799 Break this problem into two subproblems by setting (x + -13.75) equal to 24.270609799 and -24.270609799.Subproblem 1
x + -13.75 = 24.270609799 Simplifying x + -13.75 = 24.270609799 Reorder the terms: -13.75 + x = 24.270609799 Solving -13.75 + x = 24.270609799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 24.270609799 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 24.270609799 + 13.75 x = 24.270609799 + 13.75 Combine like terms: 24.270609799 + 13.75 = 38.020609799 x = 38.020609799 Simplifying x = 38.020609799Subproblem 2
x + -13.75 = -24.270609799 Simplifying x + -13.75 = -24.270609799 Reorder the terms: -13.75 + x = -24.270609799 Solving -13.75 + x = -24.270609799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -24.270609799 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -24.270609799 + 13.75 x = -24.270609799 + 13.75 Combine like terms: -24.270609799 + 13.75 = -10.520609799 x = -10.520609799 Simplifying x = -10.520609799Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.020609799, -10.520609799}
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