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Simplifying 2x2 + 13x + 9 = 1 Reorder the terms: 9 + 13x + 2x2 = 1 Solving 9 + 13x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: 9 + -1 + 13x + 2x2 = 1 + -1 Combine like terms: 9 + -1 = 8 8 + 13x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 8 + 13x + 2x2 = 0 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 = -0.688262309 x = -0.688262309 Simplifying x = -0.688262309Subproblem 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 = -5.811737691 x = -5.811737691 Simplifying x = -5.811737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.688262309, -5.811737691}
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