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Simplifying 9x2 + -26x + -40 = x2 + 9x Reorder the terms: -40 + -26x + 9x2 = x2 + 9x Reorder the terms: -40 + -26x + 9x2 = 9x + x2 Solving -40 + -26x + 9x2 = 9x + x2 Solving for variable 'x'. Reorder the terms: -40 + -26x + -9x + 9x2 + -1x2 = 9x + x2 + -9x + -1x2 Combine like terms: -26x + -9x = -35x -40 + -35x + 9x2 + -1x2 = 9x + x2 + -9x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 -40 + -35x + 8x2 = 9x + x2 + -9x + -1x2 Reorder the terms: -40 + -35x + 8x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 -40 + -35x + 8x2 = 0 + x2 + -1x2 -40 + -35x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -40 + -35x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5 + -4.375x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.375x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.375x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.375x + x2 = 0 + 5 -4.375x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.375x + x2 = 5 The x term is -4.375x. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375x + 4.78515625 + x2 = 5 + 4.78515625 Reorder the terms: 4.78515625 + -4.375x + x2 = 5 + 4.78515625 Combine like terms: 5 + 4.78515625 = 9.78515625 4.78515625 + -4.375x + x2 = 9.78515625 Factor a perfect square on the left side: (x + -2.1875)(x + -2.1875) = 9.78515625 Calculate the square root of the right side: 3.128123439 Break this problem into two subproblems by setting (x + -2.1875) equal to 3.128123439 and -3.128123439.Subproblem 1
x + -2.1875 = 3.128123439 Simplifying x + -2.1875 = 3.128123439 Reorder the terms: -2.1875 + x = 3.128123439 Solving -2.1875 + x = 3.128123439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = 3.128123439 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = 3.128123439 + 2.1875 x = 3.128123439 + 2.1875 Combine like terms: 3.128123439 + 2.1875 = 5.315623439 x = 5.315623439 Simplifying x = 5.315623439Subproblem 2
x + -2.1875 = -3.128123439 Simplifying x + -2.1875 = -3.128123439 Reorder the terms: -2.1875 + x = -3.128123439 Solving -2.1875 + x = -3.128123439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = -3.128123439 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = -3.128123439 + 2.1875 x = -3.128123439 + 2.1875 Combine like terms: -3.128123439 + 2.1875 = -0.940623439 x = -0.940623439 Simplifying x = -0.940623439Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.315623439, -0.940623439}
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