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Simplifying 2x2 + -26x + -45 = 0 Reorder the terms: -45 + -26x + 2x2 = 0 Solving -45 + -26x + 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'. -22.5 + -13x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -13x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -13x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -13x + x2 = 0 + 22.5 -13x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -13x + x2 = 22.5 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 22.5 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 22.5 + 42.25 Combine like terms: 22.5 + 42.25 = 64.75 42.25 + -13x + x2 = 64.75 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 64.75 Calculate the square root of the right side: 8.04673847 Break this problem into two subproblems by setting (x + -6.5) equal to 8.04673847 and -8.04673847.Subproblem 1
x + -6.5 = 8.04673847 Simplifying x + -6.5 = 8.04673847 Reorder the terms: -6.5 + x = 8.04673847 Solving -6.5 + x = 8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.04673847 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.04673847 + 6.5 x = 8.04673847 + 6.5 Combine like terms: 8.04673847 + 6.5 = 14.54673847 x = 14.54673847 Simplifying x = 14.54673847Subproblem 2
x + -6.5 = -8.04673847 Simplifying x + -6.5 = -8.04673847 Reorder the terms: -6.5 + x = -8.04673847 Solving -6.5 + x = -8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.04673847 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.04673847 + 6.5 x = -8.04673847 + 6.5 Combine like terms: -8.04673847 + 6.5 = -1.54673847 x = -1.54673847 Simplifying x = -1.54673847Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.54673847, -1.54673847}
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