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Simplifying 3.17x2 + -4.225x + 1.156 = 0 Reorder the terms: 1.156 + -4.225x + 3.17x2 = 0 Solving 1.156 + -4.225x + 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 + -1.332807571x + x2 = 0 Move the constant term to the right: Add '-0.3646687697' to each side of the equation. 0.3646687697 + -1.332807571x + -0.3646687697 + x2 = 0 + -0.3646687697 Reorder the terms: 0.3646687697 + -0.3646687697 + -1.332807571x + x2 = 0 + -0.3646687697 Combine like terms: 0.3646687697 + -0.3646687697 = 0.0000000000 0.0000000000 + -1.332807571x + x2 = 0 + -0.3646687697 -1.332807571x + x2 = 0 + -0.3646687697 Combine like terms: 0 + -0.3646687697 = -0.3646687697 -1.332807571x + x2 = -0.3646687697 The x term is -1.332807571x. Take half its coefficient (-0.6664037855). Square it (0.4440940053) and add it to both sides. Add '0.4440940053' to each side of the equation. -1.332807571x + 0.4440940053 + x2 = -0.3646687697 + 0.4440940053 Reorder the terms: 0.4440940053 + -1.332807571x + x2 = -0.3646687697 + 0.4440940053 Combine like terms: -0.3646687697 + 0.4440940053 = 0.0794252356 0.4440940053 + -1.332807571x + x2 = 0.0794252356 Factor a perfect square on the left side: (x + -0.6664037855)(x + -0.6664037855) = 0.0794252356 Calculate the square root of the right side: 0.281824831 Break this problem into two subproblems by setting (x + -0.6664037855) equal to 0.281824831 and -0.281824831.Subproblem 1
x + -0.6664037855 = 0.281824831 Simplifying x + -0.6664037855 = 0.281824831 Reorder the terms: -0.6664037855 + x = 0.281824831 Solving -0.6664037855 + x = 0.281824831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6664037855' to each side of the equation. -0.6664037855 + 0.6664037855 + x = 0.281824831 + 0.6664037855 Combine like terms: -0.6664037855 + 0.6664037855 = 0.0000000000 0.0000000000 + x = 0.281824831 + 0.6664037855 x = 0.281824831 + 0.6664037855 Combine like terms: 0.281824831 + 0.6664037855 = 0.9482286165 x = 0.9482286165 Simplifying x = 0.9482286165Subproblem 2
x + -0.6664037855 = -0.281824831 Simplifying x + -0.6664037855 = -0.281824831 Reorder the terms: -0.6664037855 + x = -0.281824831 Solving -0.6664037855 + x = -0.281824831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6664037855' to each side of the equation. -0.6664037855 + 0.6664037855 + x = -0.281824831 + 0.6664037855 Combine like terms: -0.6664037855 + 0.6664037855 = 0.0000000000 0.0000000000 + x = -0.281824831 + 0.6664037855 x = -0.281824831 + 0.6664037855 Combine like terms: -0.281824831 + 0.6664037855 = 0.3845789545 x = 0.3845789545 Simplifying x = 0.3845789545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9482286165, 0.3845789545}
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