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Simplifying 2x2 + -13x + 8 = 0byfactoring Reorder the terms: 8 + -13x + 2x2 = 0byfactoring Anything times zero is zero. 8 + -13x + 2x2 = 0abcfginorty Solving 8 + -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'. 4 + -6.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -6.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6.5x + x2 = 0 + -4 -6.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6.5x + x2 = -4 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 = -4 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -4 + 10.5625 Combine like terms: -4 + 10.5625 = 6.5625 10.5625 + -6.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -3.25) equal to 2.561737691 and -2.561737691.Subproblem 1
x + -3.25 = 2.561737691 Simplifying x + -3.25 = 2.561737691 Reorder the terms: -3.25 + x = 2.561737691 Solving -3.25 + x = 2.561737691 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 = 2.561737691 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.561737691 + 3.25 x = 2.561737691 + 3.25 Combine like terms: 2.561737691 + 3.25 = 5.811737691 x = 5.811737691 Simplifying x = 5.811737691Subproblem 2
x + -3.25 = -2.561737691 Simplifying x + -3.25 = -2.561737691 Reorder the terms: -3.25 + x = -2.561737691 Solving -3.25 + x = -2.561737691 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 = -2.561737691 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.561737691 + 3.25 x = -2.561737691 + 3.25 Combine like terms: -2.561737691 + 3.25 = 0.688262309 x = 0.688262309 Simplifying x = 0.688262309Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.811737691, 0.688262309}
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