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Simplifying 0 = 6x2 + -24x + 1 Reorder the terms: 0 = 1 + -24x + 6x2 Solving 0 = 1 + -24x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 24x + -6x2 = 1 + -24x + 6x2 + -1 + 24x + -6x2 Reorder the terms: -1 + 24x + -6x2 = 1 + -1 + -24x + 24x + 6x2 + -6x2 Combine like terms: 1 + -1 = 0 -1 + 24x + -6x2 = 0 + -24x + 24x + 6x2 + -6x2 -1 + 24x + -6x2 = -24x + 24x + 6x2 + -6x2 Combine like terms: -24x + 24x = 0 -1 + 24x + -6x2 = 0 + 6x2 + -6x2 -1 + 24x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -1 + 24x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.1666666667 + -4x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -4x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -4x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.1666666667 -4x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -4x + x2 = -0.1666666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.1666666667 + 4 Reorder the terms: 4 + -4x + x2 = -0.1666666667 + 4 Combine like terms: -0.1666666667 + 4 = 3.8333333333 4 + -4x + x2 = 3.8333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.8333333333 Calculate the square root of the right side: 1.957890021 Break this problem into two subproblems by setting (x + -2) equal to 1.957890021 and -1.957890021.Subproblem 1
x + -2 = 1.957890021 Simplifying x + -2 = 1.957890021 Reorder the terms: -2 + x = 1.957890021 Solving -2 + x = 1.957890021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.957890021 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.957890021 + 2 x = 1.957890021 + 2 Combine like terms: 1.957890021 + 2 = 3.957890021 x = 3.957890021 Simplifying x = 3.957890021Subproblem 2
x + -2 = -1.957890021 Simplifying x + -2 = -1.957890021 Reorder the terms: -2 + x = -1.957890021 Solving -2 + x = -1.957890021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.957890021 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.957890021 + 2 x = -1.957890021 + 2 Combine like terms: -1.957890021 + 2 = 0.042109979 x = 0.042109979 Simplifying x = 0.042109979Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.957890021, 0.042109979}
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