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Simplifying 6x2 + -36x + 5 = 0 Reorder the terms: 5 + -36x + 6x2 = 0 Solving 5 + -36x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -6x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -6x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -6x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + -0.8333333333 -6x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -6x + x2 = -0.8333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.8333333333 + 9 Reorder the terms: 9 + -6x + x2 = -0.8333333333 + 9 Combine like terms: -0.8333333333 + 9 = 8.1666666667 9 + -6x + x2 = 8.1666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.1666666667 Calculate the square root of the right side: 2.857738033 Break this problem into two subproblems by setting (x + -3) equal to 2.857738033 and -2.857738033.Subproblem 1
x + -3 = 2.857738033 Simplifying x + -3 = 2.857738033 Reorder the terms: -3 + x = 2.857738033 Solving -3 + x = 2.857738033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.857738033 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.857738033 + 3 x = 2.857738033 + 3 Combine like terms: 2.857738033 + 3 = 5.857738033 x = 5.857738033 Simplifying x = 5.857738033Subproblem 2
x + -3 = -2.857738033 Simplifying x + -3 = -2.857738033 Reorder the terms: -3 + x = -2.857738033 Solving -3 + x = -2.857738033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.857738033 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.857738033 + 3 x = -2.857738033 + 3 Combine like terms: -2.857738033 + 3 = 0.142261967 x = 0.142261967 Simplifying x = 0.142261967Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.857738033, 0.142261967}
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