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Simplifying 2x2 + 6x + -59 = 0 Reorder the terms: -59 + 6x + 2x2 = 0 Solving -59 + 6x + 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'. -29.5 + 3x + x2 = 0 Move the constant term to the right: Add '29.5' to each side of the equation. -29.5 + 3x + 29.5 + x2 = 0 + 29.5 Reorder the terms: -29.5 + 29.5 + 3x + x2 = 0 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + 3x + x2 = 0 + 29.5 3x + x2 = 0 + 29.5 Combine like terms: 0 + 29.5 = 29.5 3x + x2 = 29.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 29.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 29.5 + 2.25 Combine like terms: 29.5 + 2.25 = 31.75 2.25 + 3x + x2 = 31.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (x + 1.5) equal to 5.634713835 and -5.634713835.Subproblem 1
x + 1.5 = 5.634713835 Simplifying x + 1.5 = 5.634713835 Reorder the terms: 1.5 + x = 5.634713835 Solving 1.5 + x = 5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.634713835 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.634713835 + -1.5 x = 5.634713835 + -1.5 Combine like terms: 5.634713835 + -1.5 = 4.134713835 x = 4.134713835 Simplifying x = 4.134713835Subproblem 2
x + 1.5 = -5.634713835 Simplifying x + 1.5 = -5.634713835 Reorder the terms: 1.5 + x = -5.634713835 Solving 1.5 + x = -5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.634713835 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.634713835 + -1.5 x = -5.634713835 + -1.5 Combine like terms: -5.634713835 + -1.5 = -7.134713835 x = -7.134713835 Simplifying x = -7.134713835Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.134713835, -7.134713835}
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