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Simplifying 322.208 + 1.2454x2 = 58.2884x Solving 322.208 + 1.2454x2 = 58.2884x Solving for variable 'x'. Reorder the terms: 322.208 + -58.2884x + 1.2454x2 = 58.2884x + -58.2884x Combine like terms: 58.2884x + -58.2884x = 0.0000 322.208 + -58.2884x + 1.2454x2 = 0.0000 Begin completing the square. Divide all terms by 1.2454 the coefficient of the squared term: Divide each side by '1.2454'. 258.718484 + -46.80295487x + x2 = 0 Move the constant term to the right: Add '-258.718484' to each side of the equation. 258.718484 + -46.80295487x + -258.718484 + x2 = 0 + -258.718484 Reorder the terms: 258.718484 + -258.718484 + -46.80295487x + x2 = 0 + -258.718484 Combine like terms: 258.718484 + -258.718484 = 0.000000 0.000000 + -46.80295487x + x2 = 0 + -258.718484 -46.80295487x + x2 = 0 + -258.718484 Combine like terms: 0 + -258.718484 = -258.718484 -46.80295487x + x2 = -258.718484 The x term is -46.80295487x. Take half its coefficient (-23.40147744). Square it (547.6291464) and add it to both sides. Add '547.6291464' to each side of the equation. -46.80295487x + 547.6291464 + x2 = -258.718484 + 547.6291464 Reorder the terms: 547.6291464 + -46.80295487x + x2 = -258.718484 + 547.6291464 Combine like terms: -258.718484 + 547.6291464 = 288.9106624 547.6291464 + -46.80295487x + x2 = 288.9106624 Factor a perfect square on the left side: (x + -23.40147744)(x + -23.40147744) = 288.9106624 Calculate the square root of the right side: 16.99737222 Break this problem into two subproblems by setting (x + -23.40147744) equal to 16.99737222 and -16.99737222.Subproblem 1
x + -23.40147744 = 16.99737222 Simplifying x + -23.40147744 = 16.99737222 Reorder the terms: -23.40147744 + x = 16.99737222 Solving -23.40147744 + x = 16.99737222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.40147744' to each side of the equation. -23.40147744 + 23.40147744 + x = 16.99737222 + 23.40147744 Combine like terms: -23.40147744 + 23.40147744 = 0.00000000 0.00000000 + x = 16.99737222 + 23.40147744 x = 16.99737222 + 23.40147744 Combine like terms: 16.99737222 + 23.40147744 = 40.39884966 x = 40.39884966 Simplifying x = 40.39884966Subproblem 2
x + -23.40147744 = -16.99737222 Simplifying x + -23.40147744 = -16.99737222 Reorder the terms: -23.40147744 + x = -16.99737222 Solving -23.40147744 + x = -16.99737222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.40147744' to each side of the equation. -23.40147744 + 23.40147744 + x = -16.99737222 + 23.40147744 Combine like terms: -23.40147744 + 23.40147744 = 0.00000000 0.00000000 + x = -16.99737222 + 23.40147744 x = -16.99737222 + 23.40147744 Combine like terms: -16.99737222 + 23.40147744 = 6.40410522 x = 6.40410522 Simplifying x = 6.40410522Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.39884966, 6.40410522}
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