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Simplifying 0 = x2 + 9x + -40 Reorder the terms: 0 = -40 + 9x + x2 Solving 0 = -40 + 9x + x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + -9x + -1x2 = -40 + 9x + x2 + 40 + -9x + -1x2 Reorder the terms: 40 + -9x + -1x2 = -40 + 40 + 9x + -9x + x2 + -1x2 Combine like terms: -40 + 40 = 0 40 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2 40 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 40 + -9x + -1x2 = 0 + x2 + -1x2 40 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 9x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 9x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 9x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 9x + x2 = 0 + 40 9x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 9x + x2 = 40 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 40 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 40 + 20.25 Combine like terms: 40 + 20.25 = 60.25 20.25 + 9x + x2 = 60.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 4.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 4.5 = 7.762087348 Simplifying x + 4.5 = 7.762087348 Reorder the terms: 4.5 + x = 7.762087348 Solving 4.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 7.762087348 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.762087348 + -4.5 x = 7.762087348 + -4.5 Combine like terms: 7.762087348 + -4.5 = 3.262087348 x = 3.262087348 Simplifying x = 3.262087348Subproblem 2
x + 4.5 = -7.762087348 Simplifying x + 4.5 = -7.762087348 Reorder the terms: 4.5 + x = -7.762087348 Solving 4.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -7.762087348 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.762087348 + -4.5 x = -7.762087348 + -4.5 Combine like terms: -7.762087348 + -4.5 = -12.262087348 x = -12.262087348 Simplifying x = -12.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.262087348, -12.262087348}
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