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Simplifying 66.67x2 + 10x = 6 Reorder the terms: 10x + 66.67x2 = 6 Solving 10x + 66.67x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 10x + 66.67x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 10x + 66.67x2 = 0 Begin completing the square. Divide all terms by 66.67 the coefficient of the squared term: Divide each side by '66.67'. -0.08999550022 + 0.1499925004x + x2 = 0 Move the constant term to the right: Add '0.08999550022' to each side of the equation. -0.08999550022 + 0.1499925004x + 0.08999550022 + x2 = 0 + 0.08999550022 Reorder the terms: -0.08999550022 + 0.08999550022 + 0.1499925004x + x2 = 0 + 0.08999550022 Combine like terms: -0.08999550022 + 0.08999550022 = 0.00000000000 0.00000000000 + 0.1499925004x + x2 = 0 + 0.08999550022 0.1499925004x + x2 = 0 + 0.08999550022 Combine like terms: 0 + 0.08999550022 = 0.08999550022 0.1499925004x + x2 = 0.08999550022 The x term is 0.1499925004x. Take half its coefficient (0.0749962502). Square it (0.005624437544) and add it to both sides. Add '0.005624437544' to each side of the equation. 0.1499925004x + 0.005624437544 + x2 = 0.08999550022 + 0.005624437544 Reorder the terms: 0.005624437544 + 0.1499925004x + x2 = 0.08999550022 + 0.005624437544 Combine like terms: 0.08999550022 + 0.005624437544 = 0.095619937764 0.005624437544 + 0.1499925004x + x2 = 0.095619937764 Factor a perfect square on the left side: (x + 0.0749962502)(x + 0.0749962502) = 0.095619937764 Calculate the square root of the right side: 0.309224737 Break this problem into two subproblems by setting (x + 0.0749962502) equal to 0.309224737 and -0.309224737.Subproblem 1
x + 0.0749962502 = 0.309224737 Simplifying x + 0.0749962502 = 0.309224737 Reorder the terms: 0.0749962502 + x = 0.309224737 Solving 0.0749962502 + x = 0.309224737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0749962502' to each side of the equation. 0.0749962502 + -0.0749962502 + x = 0.309224737 + -0.0749962502 Combine like terms: 0.0749962502 + -0.0749962502 = 0.0000000000 0.0000000000 + x = 0.309224737 + -0.0749962502 x = 0.309224737 + -0.0749962502 Combine like terms: 0.309224737 + -0.0749962502 = 0.2342284868 x = 0.2342284868 Simplifying x = 0.2342284868Subproblem 2
x + 0.0749962502 = -0.309224737 Simplifying x + 0.0749962502 = -0.309224737 Reorder the terms: 0.0749962502 + x = -0.309224737 Solving 0.0749962502 + x = -0.309224737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0749962502' to each side of the equation. 0.0749962502 + -0.0749962502 + x = -0.309224737 + -0.0749962502 Combine like terms: 0.0749962502 + -0.0749962502 = 0.0000000000 0.0000000000 + x = -0.309224737 + -0.0749962502 x = -0.309224737 + -0.0749962502 Combine like terms: -0.309224737 + -0.0749962502 = -0.3842209872 x = -0.3842209872 Simplifying x = -0.3842209872Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2342284868, -0.3842209872}
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