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Simplifying 65x2 + 12x + -40 = 0 Reorder the terms: -40 + 12x + 65x2 = 0 Solving -40 + 12x + 65x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. -0.6153846154 + 0.1846153846x + x2 = 0 Move the constant term to the right: Add '0.6153846154' to each side of the equation. -0.6153846154 + 0.1846153846x + 0.6153846154 + x2 = 0 + 0.6153846154 Reorder the terms: -0.6153846154 + 0.6153846154 + 0.1846153846x + x2 = 0 + 0.6153846154 Combine like terms: -0.6153846154 + 0.6153846154 = 0.0000000000 0.0000000000 + 0.1846153846x + x2 = 0 + 0.6153846154 0.1846153846x + x2 = 0 + 0.6153846154 Combine like terms: 0 + 0.6153846154 = 0.6153846154 0.1846153846x + x2 = 0.6153846154 The x term is 0.1846153846x. Take half its coefficient (0.0923076923). Square it (0.008520710058) and add it to both sides. Add '0.008520710058' to each side of the equation. 0.1846153846x + 0.008520710058 + x2 = 0.6153846154 + 0.008520710058 Reorder the terms: 0.008520710058 + 0.1846153846x + x2 = 0.6153846154 + 0.008520710058 Combine like terms: 0.6153846154 + 0.008520710058 = 0.623905325458 0.008520710058 + 0.1846153846x + x2 = 0.623905325458 Factor a perfect square on the left side: (x + 0.0923076923)(x + 0.0923076923) = 0.623905325458 Calculate the square root of the right side: 0.789876779 Break this problem into two subproblems by setting (x + 0.0923076923) equal to 0.789876779 and -0.789876779.Subproblem 1
x + 0.0923076923 = 0.789876779 Simplifying x + 0.0923076923 = 0.789876779 Reorder the terms: 0.0923076923 + x = 0.789876779 Solving 0.0923076923 + x = 0.789876779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0923076923' to each side of the equation. 0.0923076923 + -0.0923076923 + x = 0.789876779 + -0.0923076923 Combine like terms: 0.0923076923 + -0.0923076923 = 0.0000000000 0.0000000000 + x = 0.789876779 + -0.0923076923 x = 0.789876779 + -0.0923076923 Combine like terms: 0.789876779 + -0.0923076923 = 0.6975690867 x = 0.6975690867 Simplifying x = 0.6975690867Subproblem 2
x + 0.0923076923 = -0.789876779 Simplifying x + 0.0923076923 = -0.789876779 Reorder the terms: 0.0923076923 + x = -0.789876779 Solving 0.0923076923 + x = -0.789876779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0923076923' to each side of the equation. 0.0923076923 + -0.0923076923 + x = -0.789876779 + -0.0923076923 Combine like terms: 0.0923076923 + -0.0923076923 = 0.0000000000 0.0000000000 + x = -0.789876779 + -0.0923076923 x = -0.789876779 + -0.0923076923 Combine like terms: -0.789876779 + -0.0923076923 = -0.8821844713 x = -0.8821844713 Simplifying x = -0.8821844713Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6975690867, -0.8821844713}
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