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Simplifying 2x2 + 3x + -39 = 0 Reorder the terms: -39 + 3x + 2x2 = 0 Solving -39 + 3x + 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 + 1.5x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + 1.5x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + 1.5x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + 1.5x + x2 = 0 + 19.5 1.5x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 1.5x + x2 = 19.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 19.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 19.5 + 0.5625 Combine like terms: 19.5 + 0.5625 = 20.0625 0.5625 + 1.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 0.75) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 0.75 = 4.479118217 Simplifying x + 0.75 = 4.479118217 Reorder the terms: 0.75 + x = 4.479118217 Solving 0.75 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.479118217 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.479118217 + -0.75 x = 4.479118217 + -0.75 Combine like terms: 4.479118217 + -0.75 = 3.729118217 x = 3.729118217 Simplifying x = 3.729118217Subproblem 2
x + 0.75 = -4.479118217 Simplifying x + 0.75 = -4.479118217 Reorder the terms: 0.75 + x = -4.479118217 Solving 0.75 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.479118217 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.479118217 + -0.75 x = -4.479118217 + -0.75 Combine like terms: -4.479118217 + -0.75 = -5.229118217 x = -5.229118217 Simplifying x = -5.229118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.729118217, -5.229118217}
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