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Simplifying 2x2 + -13x + -40 = 0 Reorder the terms: -40 + -13x + 2x2 = 0 Solving -40 + -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'. -20 + -6.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -6.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -6.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6.5x + x2 = 0 + 20 -6.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6.5x + x2 = 20 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 = 20 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 20 + 10.5625 Combine like terms: 20 + 10.5625 = 30.5625 10.5625 + -6.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + -3.25) equal to 5.528336097 and -5.528336097.Subproblem 1
x + -3.25 = 5.528336097 Simplifying x + -3.25 = 5.528336097 Reorder the terms: -3.25 + x = 5.528336097 Solving -3.25 + x = 5.528336097 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 = 5.528336097 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 5.528336097 + 3.25 x = 5.528336097 + 3.25 Combine like terms: 5.528336097 + 3.25 = 8.778336097 x = 8.778336097 Simplifying x = 8.778336097Subproblem 2
x + -3.25 = -5.528336097 Simplifying x + -3.25 = -5.528336097 Reorder the terms: -3.25 + x = -5.528336097 Solving -3.25 + x = -5.528336097 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 = -5.528336097 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -5.528336097 + 3.25 x = -5.528336097 + 3.25 Combine like terms: -5.528336097 + 3.25 = -2.278336097 x = -2.278336097 Simplifying x = -2.278336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.778336097, -2.278336097}
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