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Simplifying 9x2 + -40x + -320 = 0 Reorder the terms: -320 + -40x + 9x2 = 0 Solving -320 + -40x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -35.55555556 + -4.444444444x + x2 = 0 Move the constant term to the right: Add '35.55555556' to each side of the equation. -35.55555556 + -4.444444444x + 35.55555556 + x2 = 0 + 35.55555556 Reorder the terms: -35.55555556 + 35.55555556 + -4.444444444x + x2 = 0 + 35.55555556 Combine like terms: -35.55555556 + 35.55555556 = 0.00000000 0.00000000 + -4.444444444x + x2 = 0 + 35.55555556 -4.444444444x + x2 = 0 + 35.55555556 Combine like terms: 0 + 35.55555556 = 35.55555556 -4.444444444x + x2 = 35.55555556 The x term is -4.444444444x. Take half its coefficient (-2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. -4.444444444x + 4.938271604 + x2 = 35.55555556 + 4.938271604 Reorder the terms: 4.938271604 + -4.444444444x + x2 = 35.55555556 + 4.938271604 Combine like terms: 35.55555556 + 4.938271604 = 40.493827164 4.938271604 + -4.444444444x + x2 = 40.493827164 Factor a perfect square on the left side: (x + -2.222222222)(x + -2.222222222) = 40.493827164 Calculate the square root of the right side: 6.363476028 Break this problem into two subproblems by setting (x + -2.222222222) equal to 6.363476028 and -6.363476028.Subproblem 1
x + -2.222222222 = 6.363476028 Simplifying x + -2.222222222 = 6.363476028 Reorder the terms: -2.222222222 + x = 6.363476028 Solving -2.222222222 + x = 6.363476028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = 6.363476028 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 6.363476028 + 2.222222222 x = 6.363476028 + 2.222222222 Combine like terms: 6.363476028 + 2.222222222 = 8.58569825 x = 8.58569825 Simplifying x = 8.58569825Subproblem 2
x + -2.222222222 = -6.363476028 Simplifying x + -2.222222222 = -6.363476028 Reorder the terms: -2.222222222 + x = -6.363476028 Solving -2.222222222 + x = -6.363476028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = -6.363476028 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -6.363476028 + 2.222222222 x = -6.363476028 + 2.222222222 Combine like terms: -6.363476028 + 2.222222222 = -4.141253806 x = -4.141253806 Simplifying x = -4.141253806Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.58569825, -4.141253806}
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