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Simplifying 369297 = 0.6213x2 + 468.84x + 14091 Reorder the terms: 369297 = 14091 + 468.84x + 0.6213x2 Solving 369297 = 14091 + 468.84x + 0.6213x2 Solving for variable 'x'. Combine like terms: 369297 + -14091 = 355206 355206 + -468.84x + -0.6213x2 = 14091 + 468.84x + 0.6213x2 + -14091 + -468.84x + -0.6213x2 Reorder the terms: 355206 + -468.84x + -0.6213x2 = 14091 + -14091 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 14091 + -14091 = 0 355206 + -468.84x + -0.6213x2 = 0 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2 355206 + -468.84x + -0.6213x2 = 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 468.84x + -468.84x = 0.00 355206 + -468.84x + -0.6213x2 = 0.00 + 0.6213x2 + -0.6213x2 355206 + -468.84x + -0.6213x2 = 0.6213x2 + -0.6213x2 Combine like terms: 0.6213x2 + -0.6213x2 = 0.0000 355206 + -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'. -571714.1478 + 754.6112989x + x2 = 0 Move the constant term to the right: Add '571714.1478' to each side of the equation. -571714.1478 + 754.6112989x + 571714.1478 + x2 = 0 + 571714.1478 Reorder the terms: -571714.1478 + 571714.1478 + 754.6112989x + x2 = 0 + 571714.1478 Combine like terms: -571714.1478 + 571714.1478 = 0.0000 0.0000 + 754.6112989x + x2 = 0 + 571714.1478 754.6112989x + x2 = 0 + 571714.1478 Combine like terms: 0 + 571714.1478 = 571714.1478 754.6112989x + x2 = 571714.1478 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 = 571714.1478 + 142359.5531 Reorder the terms: 142359.5531 + 754.6112989x + x2 = 571714.1478 + 142359.5531 Combine like terms: 571714.1478 + 142359.5531 = 714073.7009 142359.5531 + 754.6112989x + x2 = 714073.7009 Factor a perfect square on the left side: (x + 377.3056495)(x + 377.3056495) = 714073.7009 Calculate the square root of the right side: 845.028816609 Break this problem into two subproblems by setting (x + 377.3056495) equal to 845.028816609 and -845.028816609.Subproblem 1
x + 377.3056495 = 845.028816609 Simplifying x + 377.3056495 = 845.028816609 Reorder the terms: 377.3056495 + x = 845.028816609 Solving 377.3056495 + x = 845.028816609 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 = 845.028816609 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = 845.028816609 + -377.3056495 x = 845.028816609 + -377.3056495 Combine like terms: 845.028816609 + -377.3056495 = 467.723167109 x = 467.723167109 Simplifying x = 467.723167109Subproblem 2
x + 377.3056495 = -845.028816609 Simplifying x + 377.3056495 = -845.028816609 Reorder the terms: 377.3056495 + x = -845.028816609 Solving 377.3056495 + x = -845.028816609 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 = -845.028816609 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = -845.028816609 + -377.3056495 x = -845.028816609 + -377.3056495 Combine like terms: -845.028816609 + -377.3056495 = -1222.334466109 x = -1222.334466109 Simplifying x = -1222.334466109Solution
The solution to the problem is based on the solutions from the subproblems. x = {467.723167109, -1222.334466109}
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