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Simplifying 2x2 + -4x + -55 = 0 Reorder the terms: -55 + -4x + 2x2 = 0 Solving -55 + -4x + 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'. -27.5 + -2x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -2x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -2x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -2x + x2 = 0 + 27.5 -2x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -2x + x2 = 27.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 27.5 + 1 Reorder the terms: 1 + -2x + x2 = 27.5 + 1 Combine like terms: 27.5 + 1 = 28.5 1 + -2x + x2 = 28.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (x + -1) equal to 5.338539126 and -5.338539126.Subproblem 1
x + -1 = 5.338539126 Simplifying x + -1 = 5.338539126 Reorder the terms: -1 + x = 5.338539126 Solving -1 + x = 5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.338539126 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.338539126 + 1 x = 5.338539126 + 1 Combine like terms: 5.338539126 + 1 = 6.338539126 x = 6.338539126 Simplifying x = 6.338539126Subproblem 2
x + -1 = -5.338539126 Simplifying x + -1 = -5.338539126 Reorder the terms: -1 + x = -5.338539126 Solving -1 + x = -5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.338539126 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.338539126 + 1 x = -5.338539126 + 1 Combine like terms: -5.338539126 + 1 = -4.338539126 x = -4.338539126 Simplifying x = -4.338539126Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.338539126, -4.338539126}
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