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Simplifying 2x2 + 18x + -39 = 0 Reorder the terms: -39 + 18x + 2x2 = 0 Solving -39 + 18x + 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'. -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 = 39.75 20.25 + 9x + x2 = 39.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 39.75 Calculate the square root of the right side: 6.304760106 Break this problem into two subproblems by setting (x + 4.5) equal to 6.304760106 and -6.304760106.Subproblem 1
x + 4.5 = 6.304760106 Simplifying x + 4.5 = 6.304760106 Reorder the terms: 4.5 + x = 6.304760106 Solving 4.5 + x = 6.304760106 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 = 6.304760106 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.304760106 + -4.5 x = 6.304760106 + -4.5 Combine like terms: 6.304760106 + -4.5 = 1.804760106 x = 1.804760106 Simplifying x = 1.804760106Subproblem 2
x + 4.5 = -6.304760106 Simplifying x + 4.5 = -6.304760106 Reorder the terms: 4.5 + x = -6.304760106 Solving 4.5 + x = -6.304760106 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 = -6.304760106 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.304760106 + -4.5 x = -6.304760106 + -4.5 Combine like terms: -6.304760106 + -4.5 = -10.804760106 x = -10.804760106 Simplifying x = -10.804760106Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.804760106, -10.804760106}
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