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Simplifying 2x2 + 14x + -39 = 0 Reorder the terms: -39 + 14x + 2x2 = 0 Solving -39 + 14x + 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 + 7x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + 7x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + 7x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + 7x + x2 = 0 + 19.5 7x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 7x + x2 = 19.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 19.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 19.5 + 12.25 Combine like terms: 19.5 + 12.25 = 31.75 12.25 + 7x + x2 = 31.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (x + 3.5) equal to 5.634713835 and -5.634713835.Subproblem 1
x + 3.5 = 5.634713835 Simplifying x + 3.5 = 5.634713835 Reorder the terms: 3.5 + x = 5.634713835 Solving 3.5 + x = 5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.634713835 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.634713835 + -3.5 x = 5.634713835 + -3.5 Combine like terms: 5.634713835 + -3.5 = 2.134713835 x = 2.134713835 Simplifying x = 2.134713835Subproblem 2
x + 3.5 = -5.634713835 Simplifying x + 3.5 = -5.634713835 Reorder the terms: 3.5 + x = -5.634713835 Solving 3.5 + x = -5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.634713835 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.634713835 + -3.5 x = -5.634713835 + -3.5 Combine like terms: -5.634713835 + -3.5 = -9.134713835 x = -9.134713835 Simplifying x = -9.134713835Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.134713835, -9.134713835}
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