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Simplifying 3x2 + -93x + 22 = 0 Reorder the terms: 22 + -93x + 3x2 = 0 Solving 22 + -93x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.333333333 + -31x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + -31x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + -31x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + -31x + x2 = 0 + -7.333333333 -31x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 -31x + x2 = -7.333333333 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -7.333333333 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -7.333333333 + 240.25 Combine like terms: -7.333333333 + 240.25 = 232.916666667 240.25 + -31x + x2 = 232.916666667 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 232.916666667 Calculate the square root of the right side: 15.261607604 Break this problem into two subproblems by setting (x + -15.5) equal to 15.261607604 and -15.261607604.Subproblem 1
x + -15.5 = 15.261607604 Simplifying x + -15.5 = 15.261607604 Reorder the terms: -15.5 + x = 15.261607604 Solving -15.5 + x = 15.261607604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 15.261607604 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 15.261607604 + 15.5 x = 15.261607604 + 15.5 Combine like terms: 15.261607604 + 15.5 = 30.761607604 x = 30.761607604 Simplifying x = 30.761607604Subproblem 2
x + -15.5 = -15.261607604 Simplifying x + -15.5 = -15.261607604 Reorder the terms: -15.5 + x = -15.261607604 Solving -15.5 + x = -15.261607604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -15.261607604 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -15.261607604 + 15.5 x = -15.261607604 + 15.5 Combine like terms: -15.261607604 + 15.5 = 0.238392396 x = 0.238392396 Simplifying x = 0.238392396Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.761607604, 0.238392396}
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