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Simplifying 3x2 + -36x = -83 Reorder the terms: -36x + 3x2 = -83 Solving -36x + 3x2 = -83 Solving for variable 'x'. Reorder the terms: 83 + -36x + 3x2 = -83 + 83 Combine like terms: -83 + 83 = 0 83 + -36x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 27.66666667 + -12x + x2 = 0 Move the constant term to the right: Add '-27.66666667' to each side of the equation. 27.66666667 + -12x + -27.66666667 + x2 = 0 + -27.66666667 Reorder the terms: 27.66666667 + -27.66666667 + -12x + x2 = 0 + -27.66666667 Combine like terms: 27.66666667 + -27.66666667 = 0.00000000 0.00000000 + -12x + x2 = 0 + -27.66666667 -12x + x2 = 0 + -27.66666667 Combine like terms: 0 + -27.66666667 = -27.66666667 -12x + x2 = -27.66666667 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 = -27.66666667 + 36 Reorder the terms: 36 + -12x + x2 = -27.66666667 + 36 Combine like terms: -27.66666667 + 36 = 8.33333333 36 + -12x + x2 = 8.33333333 Factor a perfect square on the left side: (x + -6)(x + -6) = 8.33333333 Calculate the square root of the right side: 2.886751345 Break this problem into two subproblems by setting (x + -6) equal to 2.886751345 and -2.886751345.Subproblem 1
x + -6 = 2.886751345 Simplifying x + -6 = 2.886751345 Reorder the terms: -6 + x = 2.886751345 Solving -6 + x = 2.886751345 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 = 2.886751345 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2.886751345 + 6 x = 2.886751345 + 6 Combine like terms: 2.886751345 + 6 = 8.886751345 x = 8.886751345 Simplifying x = 8.886751345Subproblem 2
x + -6 = -2.886751345 Simplifying x + -6 = -2.886751345 Reorder the terms: -6 + x = -2.886751345 Solving -6 + x = -2.886751345 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 = -2.886751345 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2.886751345 + 6 x = -2.886751345 + 6 Combine like terms: -2.886751345 + 6 = 3.113248655 x = 3.113248655 Simplifying x = 3.113248655Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.886751345, 3.113248655}
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