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Simplifying 3.026x2 + 377.7x + 3449 = 7605 Reorder the terms: 3449 + 377.7x + 3.026x2 = 7605 Solving 3449 + 377.7x + 3.026x2 = 7605 Solving for variable 'x'. Reorder the terms: 3449 + -7605 + 377.7x + 3.026x2 = 7605 + -7605 Combine like terms: 3449 + -7605 = -4156 -4156 + 377.7x + 3.026x2 = 7605 + -7605 Combine like terms: 7605 + -7605 = 0 -4156 + 377.7x + 3.026x2 = 0 Begin completing the square. Divide all terms by 3.026 the coefficient of the squared term: Divide each side by '3.026'. -1373.430271 + 124.8182419x + x2 = 0 Move the constant term to the right: Add '1373.430271' to each side of the equation. -1373.430271 + 124.8182419x + 1373.430271 + x2 = 0 + 1373.430271 Reorder the terms: -1373.430271 + 1373.430271 + 124.8182419x + x2 = 0 + 1373.430271 Combine like terms: -1373.430271 + 1373.430271 = 0.000000 0.000000 + 124.8182419x + x2 = 0 + 1373.430271 124.8182419x + x2 = 0 + 1373.430271 Combine like terms: 0 + 1373.430271 = 1373.430271 124.8182419x + x2 = 1373.430271 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 = 1373.430271 + 3894.898378 Reorder the terms: 3894.898378 + 124.8182419x + x2 = 1373.430271 + 3894.898378 Combine like terms: 1373.430271 + 3894.898378 = 5268.328649 3894.898378 + 124.8182419x + x2 = 5268.328649 Factor a perfect square on the left side: (x + 62.40912095)(x + 62.40912095) = 5268.328649 Calculate the square root of the right side: 72.583253227 Break this problem into two subproblems by setting (x + 62.40912095) equal to 72.583253227 and -72.583253227.Subproblem 1
x + 62.40912095 = 72.583253227 Simplifying x + 62.40912095 = 72.583253227 Reorder the terms: 62.40912095 + x = 72.583253227 Solving 62.40912095 + x = 72.583253227 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 = 72.583253227 + -62.40912095 Combine like terms: 62.40912095 + -62.40912095 = 0.00000000 0.00000000 + x = 72.583253227 + -62.40912095 x = 72.583253227 + -62.40912095 Combine like terms: 72.583253227 + -62.40912095 = 10.174132277 x = 10.174132277 Simplifying x = 10.174132277Subproblem 2
x + 62.40912095 = -72.583253227 Simplifying x + 62.40912095 = -72.583253227 Reorder the terms: 62.40912095 + x = -72.583253227 Solving 62.40912095 + x = -72.583253227 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 = -72.583253227 + -62.40912095 Combine like terms: 62.40912095 + -62.40912095 = 0.00000000 0.00000000 + x = -72.583253227 + -62.40912095 x = -72.583253227 + -62.40912095 Combine like terms: -72.583253227 + -62.40912095 = -134.992374177 x = -134.992374177 Simplifying x = -134.992374177Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.174132277, -134.992374177}
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