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Simplifying 2x2 + -13x + -55 = 0 Reorder the terms: -55 + -13x + 2x2 = 0 Solving -55 + -13x + 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 + -6.5x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -6.5x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -6.5x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -6.5x + x2 = 0 + 27.5 -6.5x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -6.5x + x2 = 27.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 27.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 27.5 + 10.5625 Combine like terms: 27.5 + 10.5625 = 38.0625 10.5625 + -6.5x + x2 = 38.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 38.0625 Calculate the square root of the right side: 6.16948134 Break this problem into two subproblems by setting (x + -3.25) equal to 6.16948134 and -6.16948134.Subproblem 1
x + -3.25 = 6.16948134 Simplifying x + -3.25 = 6.16948134 Reorder the terms: -3.25 + x = 6.16948134 Solving -3.25 + x = 6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 6.16948134 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 6.16948134 + 3.25 x = 6.16948134 + 3.25 Combine like terms: 6.16948134 + 3.25 = 9.41948134 x = 9.41948134 Simplifying x = 9.41948134Subproblem 2
x + -3.25 = -6.16948134 Simplifying x + -3.25 = -6.16948134 Reorder the terms: -3.25 + x = -6.16948134 Solving -3.25 + x = -6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -6.16948134 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -6.16948134 + 3.25 x = -6.16948134 + 3.25 Combine like terms: -6.16948134 + 3.25 = -2.91948134 x = -2.91948134 Simplifying x = -2.91948134Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.41948134, -2.91948134}
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