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Simplifying 0.000975x2 + -1.6354x + 671.40858 = 0 Reorder the terms: 671.40858 + -1.6354x + 0.000975x2 = 0 Solving 671.40858 + -1.6354x + 0.000975x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.000975 the coefficient of the squared term: Divide each side by '0.000975'. 688624.1846 + -1677.333333x + x2 = 0 Move the constant term to the right: Add '-688624.1846' to each side of the equation. 688624.1846 + -1677.333333x + -688624.1846 + x2 = 0 + -688624.1846 Reorder the terms: 688624.1846 + -688624.1846 + -1677.333333x + x2 = 0 + -688624.1846 Combine like terms: 688624.1846 + -688624.1846 = 0.0000 0.0000 + -1677.333333x + x2 = 0 + -688624.1846 -1677.333333x + x2 = 0 + -688624.1846 Combine like terms: 0 + -688624.1846 = -688624.1846 -1677.333333x + x2 = -688624.1846 The x term is -1677.333333x. Take half its coefficient (-838.6666665). Square it (703361.7775) and add it to both sides. Add '703361.7775' to each side of the equation. -1677.333333x + 703361.7775 + x2 = -688624.1846 + 703361.7775 Reorder the terms: 703361.7775 + -1677.333333x + x2 = -688624.1846 + 703361.7775 Combine like terms: -688624.1846 + 703361.7775 = 14737.5929 703361.7775 + -1677.333333x + x2 = 14737.5929 Factor a perfect square on the left side: (x + -838.6666665)(x + -838.6666665) = 14737.5929 Calculate the square root of the right side: 121.398488047 Break this problem into two subproblems by setting (x + -838.6666665) equal to 121.398488047 and -121.398488047.Subproblem 1
x + -838.6666665 = 121.398488047 Simplifying x + -838.6666665 = 121.398488047 Reorder the terms: -838.6666665 + x = 121.398488047 Solving -838.6666665 + x = 121.398488047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '838.6666665' to each side of the equation. -838.6666665 + 838.6666665 + x = 121.398488047 + 838.6666665 Combine like terms: -838.6666665 + 838.6666665 = 0.0000000 0.0000000 + x = 121.398488047 + 838.6666665 x = 121.398488047 + 838.6666665 Combine like terms: 121.398488047 + 838.6666665 = 960.065154547 x = 960.065154547 Simplifying x = 960.065154547Subproblem 2
x + -838.6666665 = -121.398488047 Simplifying x + -838.6666665 = -121.398488047 Reorder the terms: -838.6666665 + x = -121.398488047 Solving -838.6666665 + x = -121.398488047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '838.6666665' to each side of the equation. -838.6666665 + 838.6666665 + x = -121.398488047 + 838.6666665 Combine like terms: -838.6666665 + 838.6666665 = 0.0000000 0.0000000 + x = -121.398488047 + 838.6666665 x = -121.398488047 + 838.6666665 Combine like terms: -121.398488047 + 838.6666665 = 717.268178453 x = 717.268178453 Simplifying x = 717.268178453Solution
The solution to the problem is based on the solutions from the subproblems. x = {960.065154547, 717.268178453}
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