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Simplifying 2x2 + 39 = -18x Reorder the terms: 39 + 2x2 = -18x Solving 39 + 2x2 = -18x Solving for variable 'x'. Reorder the terms: 39 + 18x + 2x2 = -18x + 18x Combine like terms: -18x + 18x = 0 39 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 19.5 + 9x + x2 = 0 Move the constant term to the right: Add '-19.5' to each side of the equation. 19.5 + 9x + -19.5 + x2 = 0 + -19.5 Reorder the terms: 19.5 + -19.5 + 9x + x2 = 0 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + 9x + x2 = 0 + -19.5 9x + x2 = 0 + -19.5 Combine like terms: 0 + -19.5 = -19.5 9x + x2 = -19.5 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 = -19.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -19.5 + 20.25 Combine like terms: -19.5 + 20.25 = 0.75 20.25 + 9x + x2 = 0.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + 4.5) equal to 0.866025404 and -0.866025404.Subproblem 1
x + 4.5 = 0.866025404 Simplifying x + 4.5 = 0.866025404 Reorder the terms: 4.5 + x = 0.866025404 Solving 4.5 + x = 0.866025404 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 = 0.866025404 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 0.866025404 + -4.5 x = 0.866025404 + -4.5 Combine like terms: 0.866025404 + -4.5 = -3.633974596 x = -3.633974596 Simplifying x = -3.633974596Subproblem 2
x + 4.5 = -0.866025404 Simplifying x + 4.5 = -0.866025404 Reorder the terms: 4.5 + x = -0.866025404 Solving 4.5 + x = -0.866025404 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 = -0.866025404 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -0.866025404 + -4.5 x = -0.866025404 + -4.5 Combine like terms: -0.866025404 + -4.5 = -5.366025404 x = -5.366025404 Simplifying x = -5.366025404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.633974596, -5.366025404}
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