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Simplifying 2x2 + -13x + -2 = 0 Reorder the terms: -2 + -13x + 2x2 = 0 Solving -2 + -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'. -1 + -6.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -6.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.5x + x2 = 0 + 1 -6.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.5x + x2 = 1 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 = 1 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 1 + 10.5625 Combine like terms: 1 + 10.5625 = 11.5625 10.5625 + -6.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + -3.25) equal to 3.400367627 and -3.400367627.Subproblem 1
x + -3.25 = 3.400367627 Simplifying x + -3.25 = 3.400367627 Reorder the terms: -3.25 + x = 3.400367627 Solving -3.25 + x = 3.400367627 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 = 3.400367627 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.400367627 + 3.25 x = 3.400367627 + 3.25 Combine like terms: 3.400367627 + 3.25 = 6.650367627 x = 6.650367627 Simplifying x = 6.650367627Subproblem 2
x + -3.25 = -3.400367627 Simplifying x + -3.25 = -3.400367627 Reorder the terms: -3.25 + x = -3.400367627 Solving -3.25 + x = -3.400367627 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 = -3.400367627 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.400367627 + 3.25 x = -3.400367627 + 3.25 Combine like terms: -3.400367627 + 3.25 = -0.150367627 x = -0.150367627 Simplifying x = -0.150367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.650367627, -0.150367627}
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