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Simplifying 3.17X2 + -4.255X + 1.156 = 0 Reorder the terms: 1.156 + -4.255X + 3.17X2 = 0 Solving 1.156 + -4.255X + 3.17X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3.17 the coefficient of the squared term: Divide each side by '3.17'. 0.3646687697 + -1.342271293X + X2 = 0 Move the constant term to the right: Add '-0.3646687697' to each side of the equation. 0.3646687697 + -1.342271293X + -0.3646687697 + X2 = 0 + -0.3646687697 Reorder the terms: 0.3646687697 + -0.3646687697 + -1.342271293X + X2 = 0 + -0.3646687697 Combine like terms: 0.3646687697 + -0.3646687697 = 0.0000000000 0.0000000000 + -1.342271293X + X2 = 0 + -0.3646687697 -1.342271293X + X2 = 0 + -0.3646687697 Combine like terms: 0 + -0.3646687697 = -0.3646687697 -1.342271293X + X2 = -0.3646687697 The X term is -1.342271293X. Take half its coefficient (-0.6711356465). Square it (0.4504230560) and add it to both sides. Add '0.4504230560' to each side of the equation. -1.342271293X + 0.4504230560 + X2 = -0.3646687697 + 0.4504230560 Reorder the terms: 0.4504230560 + -1.342271293X + X2 = -0.3646687697 + 0.4504230560 Combine like terms: -0.3646687697 + 0.4504230560 = 0.0857542863 0.4504230560 + -1.342271293X + X2 = 0.0857542863 Factor a perfect square on the left side: (X + -0.6711356465)(X + -0.6711356465) = 0.0857542863 Calculate the square root of the right side: 0.292838328 Break this problem into two subproblems by setting (X + -0.6711356465) equal to 0.292838328 and -0.292838328.Subproblem 1
X + -0.6711356465 = 0.292838328 Simplifying X + -0.6711356465 = 0.292838328 Reorder the terms: -0.6711356465 + X = 0.292838328 Solving -0.6711356465 + X = 0.292838328 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6711356465' to each side of the equation. -0.6711356465 + 0.6711356465 + X = 0.292838328 + 0.6711356465 Combine like terms: -0.6711356465 + 0.6711356465 = 0.0000000000 0.0000000000 + X = 0.292838328 + 0.6711356465 X = 0.292838328 + 0.6711356465 Combine like terms: 0.292838328 + 0.6711356465 = 0.9639739745 X = 0.9639739745 Simplifying X = 0.9639739745Subproblem 2
X + -0.6711356465 = -0.292838328 Simplifying X + -0.6711356465 = -0.292838328 Reorder the terms: -0.6711356465 + X = -0.292838328 Solving -0.6711356465 + X = -0.292838328 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6711356465' to each side of the equation. -0.6711356465 + 0.6711356465 + X = -0.292838328 + 0.6711356465 Combine like terms: -0.6711356465 + 0.6711356465 = 0.0000000000 0.0000000000 + X = -0.292838328 + 0.6711356465 X = -0.292838328 + 0.6711356465 Combine like terms: -0.292838328 + 0.6711356465 = 0.3782973185 X = 0.3782973185 Simplifying X = 0.3782973185Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.9639739745, 0.3782973185}
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