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Simplifying 42x + 37x2 + -72x = 46 Reorder the terms: 42x + -72x + 37x2 = 46 Combine like terms: 42x + -72x = -30x -30x + 37x2 = 46 Solving -30x + 37x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + -30x + 37x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -30x + 37x2 = 0 Begin completing the square. Divide all terms by 37 the coefficient of the squared term: Divide each side by '37'. -1.243243243 + -0.8108108108x + x2 = 0 Move the constant term to the right: Add '1.243243243' to each side of the equation. -1.243243243 + -0.8108108108x + 1.243243243 + x2 = 0 + 1.243243243 Reorder the terms: -1.243243243 + 1.243243243 + -0.8108108108x + x2 = 0 + 1.243243243 Combine like terms: -1.243243243 + 1.243243243 = 0.000000000 0.000000000 + -0.8108108108x + x2 = 0 + 1.243243243 -0.8108108108x + x2 = 0 + 1.243243243 Combine like terms: 0 + 1.243243243 = 1.243243243 -0.8108108108x + x2 = 1.243243243 The x term is -0.8108108108x. Take half its coefficient (-0.4054054054). Square it (0.1643535427) and add it to both sides. Add '0.1643535427' to each side of the equation. -0.8108108108x + 0.1643535427 + x2 = 1.243243243 + 0.1643535427 Reorder the terms: 0.1643535427 + -0.8108108108x + x2 = 1.243243243 + 0.1643535427 Combine like terms: 1.243243243 + 0.1643535427 = 1.4075967857 0.1643535427 + -0.8108108108x + x2 = 1.4075967857 Factor a perfect square on the left side: (x + -0.4054054054)(x + -0.4054054054) = 1.4075967857 Calculate the square root of the right side: 1.186421841 Break this problem into two subproblems by setting (x + -0.4054054054) equal to 1.186421841 and -1.186421841.Subproblem 1
x + -0.4054054054 = 1.186421841 Simplifying x + -0.4054054054 = 1.186421841 Reorder the terms: -0.4054054054 + x = 1.186421841 Solving -0.4054054054 + x = 1.186421841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4054054054' to each side of the equation. -0.4054054054 + 0.4054054054 + x = 1.186421841 + 0.4054054054 Combine like terms: -0.4054054054 + 0.4054054054 = 0.0000000000 0.0000000000 + x = 1.186421841 + 0.4054054054 x = 1.186421841 + 0.4054054054 Combine like terms: 1.186421841 + 0.4054054054 = 1.5918272464 x = 1.5918272464 Simplifying x = 1.5918272464Subproblem 2
x + -0.4054054054 = -1.186421841 Simplifying x + -0.4054054054 = -1.186421841 Reorder the terms: -0.4054054054 + x = -1.186421841 Solving -0.4054054054 + x = -1.186421841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4054054054' to each side of the equation. -0.4054054054 + 0.4054054054 + x = -1.186421841 + 0.4054054054 Combine like terms: -0.4054054054 + 0.4054054054 = 0.0000000000 0.0000000000 + x = -1.186421841 + 0.4054054054 x = -1.186421841 + 0.4054054054 Combine like terms: -1.186421841 + 0.4054054054 = -0.7810164356 x = -0.7810164356 Simplifying x = -0.7810164356Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5918272464, -0.7810164356}
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