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Simplifying 0.0825(x2) + -0.9220(x) + 1.713 = 0 Reorder the terms: 1.713 + -0.9220x + 0.0825x2 = 0 Solving 1.713 + -0.9220x + 0.0825x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0825 the coefficient of the squared term: Divide each side by '0.0825'. 20.76363636 + -11.17575758x + x2 = 0 Move the constant term to the right: Add '-20.76363636' to each side of the equation. 20.76363636 + -11.17575758x + -20.76363636 + x2 = 0 + -20.76363636 Reorder the terms: 20.76363636 + -20.76363636 + -11.17575758x + x2 = 0 + -20.76363636 Combine like terms: 20.76363636 + -20.76363636 = 0.00000000 0.00000000 + -11.17575758x + x2 = 0 + -20.76363636 -11.17575758x + x2 = 0 + -20.76363636 Combine like terms: 0 + -20.76363636 = -20.76363636 -11.17575758x + x2 = -20.76363636 The x term is -11.17575758x. Take half its coefficient (-5.58787879). Square it (31.22438937) and add it to both sides. Add '31.22438937' to each side of the equation. -11.17575758x + 31.22438937 + x2 = -20.76363636 + 31.22438937 Reorder the terms: 31.22438937 + -11.17575758x + x2 = -20.76363636 + 31.22438937 Combine like terms: -20.76363636 + 31.22438937 = 10.46075301 31.22438937 + -11.17575758x + x2 = 10.46075301 Factor a perfect square on the left side: (x + -5.58787879)(x + -5.58787879) = 10.46075301 Calculate the square root of the right side: 3.234308738 Break this problem into two subproblems by setting (x + -5.58787879) equal to 3.234308738 and -3.234308738.Subproblem 1
x + -5.58787879 = 3.234308738 Simplifying x + -5.58787879 = 3.234308738 Reorder the terms: -5.58787879 + x = 3.234308738 Solving -5.58787879 + x = 3.234308738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.58787879' to each side of the equation. -5.58787879 + 5.58787879 + x = 3.234308738 + 5.58787879 Combine like terms: -5.58787879 + 5.58787879 = 0.00000000 0.00000000 + x = 3.234308738 + 5.58787879 x = 3.234308738 + 5.58787879 Combine like terms: 3.234308738 + 5.58787879 = 8.822187528 x = 8.822187528 Simplifying x = 8.822187528Subproblem 2
x + -5.58787879 = -3.234308738 Simplifying x + -5.58787879 = -3.234308738 Reorder the terms: -5.58787879 + x = -3.234308738 Solving -5.58787879 + x = -3.234308738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.58787879' to each side of the equation. -5.58787879 + 5.58787879 + x = -3.234308738 + 5.58787879 Combine like terms: -5.58787879 + 5.58787879 = 0.00000000 0.00000000 + x = -3.234308738 + 5.58787879 x = -3.234308738 + 5.58787879 Combine like terms: -3.234308738 + 5.58787879 = 2.353570052 x = 2.353570052 Simplifying x = 2.353570052Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.822187528, 2.353570052}
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