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Simplifying 3x2 + -36x = 26 Reorder the terms: -36x + 3x2 = 26 Solving -36x + 3x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -36x + 3x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -36x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.666666667 + -12x + x2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -12x + 8.666666667 + x2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -12x + x2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -12x + x2 = 0 + 8.666666667 -12x + x2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -12x + x2 = 8.666666667 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 8.666666667 + 36 Reorder the terms: 36 + -12x + x2 = 8.666666667 + 36 Combine like terms: 8.666666667 + 36 = 44.666666667 36 + -12x + x2 = 44.666666667 Factor a perfect square on the left side: (x + -6)(x + -6) = 44.666666667 Calculate the square root of the right side: 6.683312552 Break this problem into two subproblems by setting (x + -6) equal to 6.683312552 and -6.683312552.Subproblem 1
x + -6 = 6.683312552 Simplifying x + -6 = 6.683312552 Reorder the terms: -6 + x = 6.683312552 Solving -6 + x = 6.683312552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.683312552 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.683312552 + 6 x = 6.683312552 + 6 Combine like terms: 6.683312552 + 6 = 12.683312552 x = 12.683312552 Simplifying x = 12.683312552Subproblem 2
x + -6 = -6.683312552 Simplifying x + -6 = -6.683312552 Reorder the terms: -6 + x = -6.683312552 Solving -6 + x = -6.683312552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.683312552 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.683312552 + 6 x = -6.683312552 + 6 Combine like terms: -6.683312552 + 6 = -0.683312552 x = -0.683312552 Simplifying x = -0.683312552Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.683312552, -0.683312552}
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