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Simplifying 3x2 + -36x + 64 = 0 Reorder the terms: 64 + -36x + 3x2 = 0 Solving 64 + -36x + 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'. 21.33333333 + -12x + x2 = 0 Move the constant term to the right: Add '-21.33333333' to each side of the equation. 21.33333333 + -12x + -21.33333333 + x2 = 0 + -21.33333333 Reorder the terms: 21.33333333 + -21.33333333 + -12x + x2 = 0 + -21.33333333 Combine like terms: 21.33333333 + -21.33333333 = 0.00000000 0.00000000 + -12x + x2 = 0 + -21.33333333 -12x + x2 = 0 + -21.33333333 Combine like terms: 0 + -21.33333333 = -21.33333333 -12x + x2 = -21.33333333 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 = -21.33333333 + 36 Reorder the terms: 36 + -12x + x2 = -21.33333333 + 36 Combine like terms: -21.33333333 + 36 = 14.66666667 36 + -12x + x2 = 14.66666667 Factor a perfect square on the left side: (x + -6)(x + -6) = 14.66666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (x + -6) equal to 3.829708431 and -3.829708431.Subproblem 1
x + -6 = 3.829708431 Simplifying x + -6 = 3.829708431 Reorder the terms: -6 + x = 3.829708431 Solving -6 + x = 3.829708431 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 = 3.829708431 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.829708431 + 6 x = 3.829708431 + 6 Combine like terms: 3.829708431 + 6 = 9.829708431 x = 9.829708431 Simplifying x = 9.829708431Subproblem 2
x + -6 = -3.829708431 Simplifying x + -6 = -3.829708431 Reorder the terms: -6 + x = -3.829708431 Solving -6 + x = -3.829708431 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 = -3.829708431 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.829708431 + 6 x = -3.829708431 + 6 Combine like terms: -3.829708431 + 6 = 2.170291569 x = 2.170291569 Simplifying x = 2.170291569Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.829708431, 2.170291569}
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