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Simplifying 4.42x2 = 20.115x + 44.957 Reorder the terms: 4.42x2 = 44.957 + 20.115x Solving 4.42x2 = 44.957 + 20.115x Solving for variable 'x'. Reorder the terms: -44.957 + -20.115x + 4.42x2 = 44.957 + 20.115x + -44.957 + -20.115x Reorder the terms: -44.957 + -20.115x + 4.42x2 = 44.957 + -44.957 + 20.115x + -20.115x Combine like terms: 44.957 + -44.957 = 0.000 -44.957 + -20.115x + 4.42x2 = 0.000 + 20.115x + -20.115x -44.957 + -20.115x + 4.42x2 = 20.115x + -20.115x Combine like terms: 20.115x + -20.115x = 0.000 -44.957 + -20.115x + 4.42x2 = 0.000 Begin completing the square. Divide all terms by 4.42 the coefficient of the squared term: Divide each side by '4.42'. -10.17126697 + -4.550904977x + x2 = 0.0 Move the constant term to the right: Add '10.17126697' to each side of the equation. -10.17126697 + -4.550904977x + 10.17126697 + x2 = 0.0 + 10.17126697 Reorder the terms: -10.17126697 + 10.17126697 + -4.550904977x + x2 = 0.0 + 10.17126697 Combine like terms: -10.17126697 + 10.17126697 = 0.00000000 0.00000000 + -4.550904977x + x2 = 0.0 + 10.17126697 -4.550904977x + x2 = 0.0 + 10.17126697 Combine like terms: 0.0 + 10.17126697 = 10.17126697 -4.550904977x + x2 = 10.17126697 The x term is -4.550904977x. Take half its coefficient (-2.275452489). Square it (5.177684030) and add it to both sides. Add '5.177684030' to each side of the equation. -4.550904977x + 5.177684030 + x2 = 10.17126697 + 5.177684030 Reorder the terms: 5.177684030 + -4.550904977x + x2 = 10.17126697 + 5.177684030 Combine like terms: 10.17126697 + 5.177684030 = 15.348951 5.177684030 + -4.550904977x + x2 = 15.348951 Factor a perfect square on the left side: (x + -2.275452489)(x + -2.275452489) = 15.348951 Calculate the square root of the right side: 3.91777373 Break this problem into two subproblems by setting (x + -2.275452489) equal to 3.91777373 and -3.91777373.Subproblem 1
x + -2.275452489 = 3.91777373 Simplifying x + -2.275452489 = 3.91777373 Reorder the terms: -2.275452489 + x = 3.91777373 Solving -2.275452489 + x = 3.91777373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.275452489' to each side of the equation. -2.275452489 + 2.275452489 + x = 3.91777373 + 2.275452489 Combine like terms: -2.275452489 + 2.275452489 = 0.000000000 0.000000000 + x = 3.91777373 + 2.275452489 x = 3.91777373 + 2.275452489 Combine like terms: 3.91777373 + 2.275452489 = 6.193226219 x = 6.193226219 Simplifying x = 6.193226219Subproblem 2
x + -2.275452489 = -3.91777373 Simplifying x + -2.275452489 = -3.91777373 Reorder the terms: -2.275452489 + x = -3.91777373 Solving -2.275452489 + x = -3.91777373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.275452489' to each side of the equation. -2.275452489 + 2.275452489 + x = -3.91777373 + 2.275452489 Combine like terms: -2.275452489 + 2.275452489 = 0.000000000 0.000000000 + x = -3.91777373 + 2.275452489 x = -3.91777373 + 2.275452489 Combine like terms: -3.91777373 + 2.275452489 = -1.642321241 x = -1.642321241 Simplifying x = -1.642321241Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.193226219, -1.642321241}
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