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Simplifying 143695 = 0.6213x2 + 468.84x + 14091 Reorder the terms: 143695 = 14091 + 468.84x + 0.6213x2 Solving 143695 = 14091 + 468.84x + 0.6213x2 Solving for variable 'x'. Combine like terms: 143695 + -14091 = 129604 129604 + -468.84x + -0.6213x2 = 14091 + 468.84x + 0.6213x2 + -14091 + -468.84x + -0.6213x2 Reorder the terms: 129604 + -468.84x + -0.6213x2 = 14091 + -14091 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 14091 + -14091 = 0 129604 + -468.84x + -0.6213x2 = 0 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2 129604 + -468.84x + -0.6213x2 = 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 468.84x + -468.84x = 0.00 129604 + -468.84x + -0.6213x2 = 0.00 + 0.6213x2 + -0.6213x2 129604 + -468.84x + -0.6213x2 = 0.6213x2 + -0.6213x2 Combine like terms: 0.6213x2 + -0.6213x2 = 0.0000 129604 + -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'. -208601.3198 + 754.6112989x + x2 = 0 Move the constant term to the right: Add '208601.3198' to each side of the equation. -208601.3198 + 754.6112989x + 208601.3198 + x2 = 0 + 208601.3198 Reorder the terms: -208601.3198 + 208601.3198 + 754.6112989x + x2 = 0 + 208601.3198 Combine like terms: -208601.3198 + 208601.3198 = 0.0000 0.0000 + 754.6112989x + x2 = 0 + 208601.3198 754.6112989x + x2 = 0 + 208601.3198 Combine like terms: 0 + 208601.3198 = 208601.3198 754.6112989x + x2 = 208601.3198 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 = 208601.3198 + 142359.5531 Reorder the terms: 142359.5531 + 754.6112989x + x2 = 208601.3198 + 142359.5531 Combine like terms: 208601.3198 + 142359.5531 = 350960.8729 142359.5531 + 754.6112989x + x2 = 350960.8729 Factor a perfect square on the left side: (x + 377.3056495)(x + 377.3056495) = 350960.8729 Calculate the square root of the right side: 592.419507528 Break this problem into two subproblems by setting (x + 377.3056495) equal to 592.419507528 and -592.419507528.Subproblem 1
x + 377.3056495 = 592.419507528 Simplifying x + 377.3056495 = 592.419507528 Reorder the terms: 377.3056495 + x = 592.419507528 Solving 377.3056495 + x = 592.419507528 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 = 592.419507528 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = 592.419507528 + -377.3056495 x = 592.419507528 + -377.3056495 Combine like terms: 592.419507528 + -377.3056495 = 215.113858028 x = 215.113858028 Simplifying x = 215.113858028Subproblem 2
x + 377.3056495 = -592.419507528 Simplifying x + 377.3056495 = -592.419507528 Reorder the terms: 377.3056495 + x = -592.419507528 Solving 377.3056495 + x = -592.419507528 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 = -592.419507528 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = -592.419507528 + -377.3056495 x = -592.419507528 + -377.3056495 Combine like terms: -592.419507528 + -377.3056495 = -969.725157028 x = -969.725157028 Simplifying x = -969.725157028Solution
The solution to the problem is based on the solutions from the subproblems. x = {215.113858028, -969.725157028}
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