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Simplifying 45x2 + 57x + -2314 = 0 Reorder the terms: -2314 + 57x + 45x2 = 0 Solving -2314 + 57x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -51.42222222 + 1.266666667x + x2 = 0 Move the constant term to the right: Add '51.42222222' to each side of the equation. -51.42222222 + 1.266666667x + 51.42222222 + x2 = 0 + 51.42222222 Reorder the terms: -51.42222222 + 51.42222222 + 1.266666667x + x2 = 0 + 51.42222222 Combine like terms: -51.42222222 + 51.42222222 = 0.00000000 0.00000000 + 1.266666667x + x2 = 0 + 51.42222222 1.266666667x + x2 = 0 + 51.42222222 Combine like terms: 0 + 51.42222222 = 51.42222222 1.266666667x + x2 = 51.42222222 The x term is 1.266666667x. Take half its coefficient (0.6333333335). Square it (0.4011111113) and add it to both sides. Add '0.4011111113' to each side of the equation. 1.266666667x + 0.4011111113 + x2 = 51.42222222 + 0.4011111113 Reorder the terms: 0.4011111113 + 1.266666667x + x2 = 51.42222222 + 0.4011111113 Combine like terms: 51.42222222 + 0.4011111113 = 51.8233333313 0.4011111113 + 1.266666667x + x2 = 51.8233333313 Factor a perfect square on the left side: (x + 0.6333333335)(x + 0.6333333335) = 51.8233333313 Calculate the square root of the right side: 7.198842499 Break this problem into two subproblems by setting (x + 0.6333333335) equal to 7.198842499 and -7.198842499.Subproblem 1
x + 0.6333333335 = 7.198842499 Simplifying x + 0.6333333335 = 7.198842499 Reorder the terms: 0.6333333335 + x = 7.198842499 Solving 0.6333333335 + x = 7.198842499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6333333335' to each side of the equation. 0.6333333335 + -0.6333333335 + x = 7.198842499 + -0.6333333335 Combine like terms: 0.6333333335 + -0.6333333335 = 0.0000000000 0.0000000000 + x = 7.198842499 + -0.6333333335 x = 7.198842499 + -0.6333333335 Combine like terms: 7.198842499 + -0.6333333335 = 6.5655091655 x = 6.5655091655 Simplifying x = 6.5655091655Subproblem 2
x + 0.6333333335 = -7.198842499 Simplifying x + 0.6333333335 = -7.198842499 Reorder the terms: 0.6333333335 + x = -7.198842499 Solving 0.6333333335 + x = -7.198842499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6333333335' to each side of the equation. 0.6333333335 + -0.6333333335 + x = -7.198842499 + -0.6333333335 Combine like terms: 0.6333333335 + -0.6333333335 = 0.0000000000 0.0000000000 + x = -7.198842499 + -0.6333333335 x = -7.198842499 + -0.6333333335 Combine like terms: -7.198842499 + -0.6333333335 = -7.8321758325 x = -7.8321758325 Simplifying x = -7.8321758325Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.5655091655, -7.8321758325}
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