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Simplifying 4x2 + -20x + -55 = 0 Reorder the terms: -55 + -20x + 4x2 = 0 Solving -55 + -20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.75 + -5x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + -5x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + -5x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + -5x + x2 = 0 + 13.75 -5x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 -5x + x2 = 13.75 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 13.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 13.75 + 6.25 Combine like terms: 13.75 + 6.25 = 20 6.25 + -5x + x2 = 20 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -2.5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -2.5 = 4.472135955 Simplifying x + -2.5 = 4.472135955 Reorder the terms: -2.5 + x = 4.472135955 Solving -2.5 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.472135955 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.472135955 + 2.5 x = 4.472135955 + 2.5 Combine like terms: 4.472135955 + 2.5 = 6.972135955 x = 6.972135955 Simplifying x = 6.972135955Subproblem 2
x + -2.5 = -4.472135955 Simplifying x + -2.5 = -4.472135955 Reorder the terms: -2.5 + x = -4.472135955 Solving -2.5 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.472135955 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.472135955 + 2.5 x = -4.472135955 + 2.5 Combine like terms: -4.472135955 + 2.5 = -1.972135955 x = -1.972135955 Simplifying x = -1.972135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.972135955, -1.972135955}
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