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Simplifying -14091 = 0.6213x2 + 468.84x Reorder the terms: -14091 = 468.84x + 0.6213x2 Solving -14091 = 468.84x + 0.6213x2 Solving for variable 'x'. Reorder the terms: -14091 + -468.84x + -0.6213x2 = 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 468.84x + -468.84x = 0.00 -14091 + -468.84x + -0.6213x2 = 0.00 + 0.6213x2 + -0.6213x2 -14091 + -468.84x + -0.6213x2 = 0.6213x2 + -0.6213x2 Combine like terms: 0.6213x2 + -0.6213x2 = 0.0000 -14091 + -468.84x + -0.6213x2 = 0.0000 Begin completing the square. Divide all terms by -0.6213 the coefficient of the squared term: Divide each side by '-0.6213'. 22679.8648 + 754.6112989x + x2 = 0 Move the constant term to the right: Add '-22679.8648' to each side of the equation. 22679.8648 + 754.6112989x + -22679.8648 + x2 = 0 + -22679.8648 Reorder the terms: 22679.8648 + -22679.8648 + 754.6112989x + x2 = 0 + -22679.8648 Combine like terms: 22679.8648 + -22679.8648 = 0.0000 0.0000 + 754.6112989x + x2 = 0 + -22679.8648 754.6112989x + x2 = 0 + -22679.8648 Combine like terms: 0 + -22679.8648 = -22679.8648 754.6112989x + x2 = -22679.8648 The x term is 754.6112989x. Take half its coefficient (377.3056495). Square it (142359.5531) and add it to both sides. Add '142359.5531' to each side of the equation. 754.6112989x + 142359.5531 + x2 = -22679.8648 + 142359.5531 Reorder the terms: 142359.5531 + 754.6112989x + x2 = -22679.8648 + 142359.5531 Combine like terms: -22679.8648 + 142359.5531 = 119679.6883 142359.5531 + 754.6112989x + x2 = 119679.6883 Factor a perfect square on the left side: (x + 377.3056495)(x + 377.3056495) = 119679.6883 Calculate the square root of the right side: 345.947522465 Break this problem into two subproblems by setting (x + 377.3056495) equal to 345.947522465 and -345.947522465.Subproblem 1
x + 377.3056495 = 345.947522465 Simplifying x + 377.3056495 = 345.947522465 Reorder the terms: 377.3056495 + x = 345.947522465 Solving 377.3056495 + x = 345.947522465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-377.3056495' to each side of the equation. 377.3056495 + -377.3056495 + x = 345.947522465 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = 345.947522465 + -377.3056495 x = 345.947522465 + -377.3056495 Combine like terms: 345.947522465 + -377.3056495 = -31.358127035 x = -31.358127035 Simplifying x = -31.358127035Subproblem 2
x + 377.3056495 = -345.947522465 Simplifying x + 377.3056495 = -345.947522465 Reorder the terms: 377.3056495 + x = -345.947522465 Solving 377.3056495 + x = -345.947522465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-377.3056495' to each side of the equation. 377.3056495 + -377.3056495 + x = -345.947522465 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = -345.947522465 + -377.3056495 x = -345.947522465 + -377.3056495 Combine like terms: -345.947522465 + -377.3056495 = -723.253171965 x = -723.253171965 Simplifying x = -723.253171965Solution
The solution to the problem is based on the solutions from the subproblems. x = {-31.358127035, -723.253171965}
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