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Simplifying 3.026x2 + 377.7x + -7605 = 0 Reorder the terms: -7605 + 377.7x + 3.026x2 = 0 Solving -7605 + 377.7x + 3.026x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.026 the coefficient of the squared term: Divide each side by '3.026'. -2513.218771 + 124.8182419x + x2 = 0 Move the constant term to the right: Add '2513.218771' to each side of the equation. -2513.218771 + 124.8182419x + 2513.218771 + x2 = 0 + 2513.218771 Reorder the terms: -2513.218771 + 2513.218771 + 124.8182419x + x2 = 0 + 2513.218771 Combine like terms: -2513.218771 + 2513.218771 = 0.000000 0.000000 + 124.8182419x + x2 = 0 + 2513.218771 124.8182419x + x2 = 0 + 2513.218771 Combine like terms: 0 + 2513.218771 = 2513.218771 124.8182419x + x2 = 2513.218771 The x term is 124.8182419x. Take half its coefficient (62.40912095). Square it (3894.898378) and add it to both sides. Add '3894.898378' to each side of the equation. 124.8182419x + 3894.898378 + x2 = 2513.218771 + 3894.898378 Reorder the terms: 3894.898378 + 124.8182419x + x2 = 2513.218771 + 3894.898378 Combine like terms: 2513.218771 + 3894.898378 = 6408.117149 3894.898378 + 124.8182419x + x2 = 6408.117149 Factor a perfect square on the left side: (x + 62.40912095)(x + 62.40912095) = 6408.117149 Calculate the square root of the right side: 80.050716105 Break this problem into two subproblems by setting (x + 62.40912095) equal to 80.050716105 and -80.050716105.Subproblem 1
x + 62.40912095 = 80.050716105 Simplifying x + 62.40912095 = 80.050716105 Reorder the terms: 62.40912095 + x = 80.050716105 Solving 62.40912095 + x = 80.050716105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.40912095' to each side of the equation. 62.40912095 + -62.40912095 + x = 80.050716105 + -62.40912095 Combine like terms: 62.40912095 + -62.40912095 = 0.00000000 0.00000000 + x = 80.050716105 + -62.40912095 x = 80.050716105 + -62.40912095 Combine like terms: 80.050716105 + -62.40912095 = 17.641595155 x = 17.641595155 Simplifying x = 17.641595155Subproblem 2
x + 62.40912095 = -80.050716105 Simplifying x + 62.40912095 = -80.050716105 Reorder the terms: 62.40912095 + x = -80.050716105 Solving 62.40912095 + x = -80.050716105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.40912095' to each side of the equation. 62.40912095 + -62.40912095 + x = -80.050716105 + -62.40912095 Combine like terms: 62.40912095 + -62.40912095 = 0.00000000 0.00000000 + x = -80.050716105 + -62.40912095 x = -80.050716105 + -62.40912095 Combine like terms: -80.050716105 + -62.40912095 = -142.459837055 x = -142.459837055 Simplifying x = -142.459837055Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.641595155, -142.459837055}
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