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Simplifying 45.8x2 + -199.2x + 199.2 = 0 Reorder the terms: 199.2 + -199.2x + 45.8x2 = 0 Solving 199.2 + -199.2x + 45.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45.8 the coefficient of the squared term: Divide each side by '45.8'. 4.349344978 + -4.349344978x + x2 = 0 Move the constant term to the right: Add '-4.349344978' to each side of the equation. 4.349344978 + -4.349344978x + -4.349344978 + x2 = 0 + -4.349344978 Reorder the terms: 4.349344978 + -4.349344978 + -4.349344978x + x2 = 0 + -4.349344978 Combine like terms: 4.349344978 + -4.349344978 = 0.000000000 0.000000000 + -4.349344978x + x2 = 0 + -4.349344978 -4.349344978x + x2 = 0 + -4.349344978 Combine like terms: 0 + -4.349344978 = -4.349344978 -4.349344978x + x2 = -4.349344978 The x term is -4.349344978x. Take half its coefficient (-2.174672489). Square it (4.729200434) and add it to both sides. Add '4.729200434' to each side of the equation. -4.349344978x + 4.729200434 + x2 = -4.349344978 + 4.729200434 Reorder the terms: 4.729200434 + -4.349344978x + x2 = -4.349344978 + 4.729200434 Combine like terms: -4.349344978 + 4.729200434 = 0.379855456 4.729200434 + -4.349344978x + x2 = 0.379855456 Factor a perfect square on the left side: (x + -2.174672489)(x + -2.174672489) = 0.379855456 Calculate the square root of the right side: 0.616324148 Break this problem into two subproblems by setting (x + -2.174672489) equal to 0.616324148 and -0.616324148.Subproblem 1
x + -2.174672489 = 0.616324148 Simplifying x + -2.174672489 = 0.616324148 Reorder the terms: -2.174672489 + x = 0.616324148 Solving -2.174672489 + x = 0.616324148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.174672489' to each side of the equation. -2.174672489 + 2.174672489 + x = 0.616324148 + 2.174672489 Combine like terms: -2.174672489 + 2.174672489 = 0.000000000 0.000000000 + x = 0.616324148 + 2.174672489 x = 0.616324148 + 2.174672489 Combine like terms: 0.616324148 + 2.174672489 = 2.790996637 x = 2.790996637 Simplifying x = 2.790996637Subproblem 2
x + -2.174672489 = -0.616324148 Simplifying x + -2.174672489 = -0.616324148 Reorder the terms: -2.174672489 + x = -0.616324148 Solving -2.174672489 + x = -0.616324148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.174672489' to each side of the equation. -2.174672489 + 2.174672489 + x = -0.616324148 + 2.174672489 Combine like terms: -2.174672489 + 2.174672489 = 0.000000000 0.000000000 + x = -0.616324148 + 2.174672489 x = -0.616324148 + 2.174672489 Combine like terms: -0.616324148 + 2.174672489 = 1.558348341 x = 1.558348341 Simplifying x = 1.558348341Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.790996637, 1.558348341}
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