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Simplifying 3x2 + -36x + -10 = 0 Reorder the terms: -10 + -36x + 3x2 = 0 Solving -10 + -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'. -3.333333333 + -12x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -12x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -12x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -12x + x2 = 0 + 3.333333333 -12x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -12x + x2 = 3.333333333 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 = 3.333333333 + 36 Reorder the terms: 36 + -12x + x2 = 3.333333333 + 36 Combine like terms: 3.333333333 + 36 = 39.333333333 36 + -12x + x2 = 39.333333333 Factor a perfect square on the left side: (x + -6)(x + -6) = 39.333333333 Calculate the square root of the right side: 6.271629241 Break this problem into two subproblems by setting (x + -6) equal to 6.271629241 and -6.271629241.Subproblem 1
x + -6 = 6.271629241 Simplifying x + -6 = 6.271629241 Reorder the terms: -6 + x = 6.271629241 Solving -6 + x = 6.271629241 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 = 6.271629241 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.271629241 + 6 x = 6.271629241 + 6 Combine like terms: 6.271629241 + 6 = 12.271629241 x = 12.271629241 Simplifying x = 12.271629241Subproblem 2
x + -6 = -6.271629241 Simplifying x + -6 = -6.271629241 Reorder the terms: -6 + x = -6.271629241 Solving -6 + x = -6.271629241 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 = -6.271629241 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.271629241 + 6 x = -6.271629241 + 6 Combine like terms: -6.271629241 + 6 = -0.271629241 x = -0.271629241 Simplifying x = -0.271629241Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.271629241, -0.271629241}
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