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Simplifying 66.67x2 + 50x = 6 Reorder the terms: 50x + 66.67x2 = 6 Solving 50x + 66.67x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 50x + 66.67x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 50x + 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 + 0.7499625019x + x2 = 0 Move the constant term to the right: Add '0.08999550022' to each side of the equation. -0.08999550022 + 0.7499625019x + 0.08999550022 + x2 = 0 + 0.08999550022 Reorder the terms: -0.08999550022 + 0.08999550022 + 0.7499625019x + x2 = 0 + 0.08999550022 Combine like terms: -0.08999550022 + 0.08999550022 = 0.00000000000 0.00000000000 + 0.7499625019x + x2 = 0 + 0.08999550022 0.7499625019x + x2 = 0 + 0.08999550022 Combine like terms: 0 + 0.08999550022 = 0.08999550022 0.7499625019x + x2 = 0.08999550022 The x term is 0.7499625019x. Take half its coefficient (0.374981251). Square it (0.1406109386) and add it to both sides. Add '0.1406109386' to each side of the equation. 0.7499625019x + 0.1406109386 + x2 = 0.08999550022 + 0.1406109386 Reorder the terms: 0.1406109386 + 0.7499625019x + x2 = 0.08999550022 + 0.1406109386 Combine like terms: 0.08999550022 + 0.1406109386 = 0.23060643882 0.1406109386 + 0.7499625019x + x2 = 0.23060643882 Factor a perfect square on the left side: (x + 0.374981251)(x + 0.374981251) = 0.23060643882 Calculate the square root of the right side: 0.480214992 Break this problem into two subproblems by setting (x + 0.374981251) equal to 0.480214992 and -0.480214992.Subproblem 1
x + 0.374981251 = 0.480214992 Simplifying x + 0.374981251 = 0.480214992 Reorder the terms: 0.374981251 + x = 0.480214992 Solving 0.374981251 + x = 0.480214992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.374981251' to each side of the equation. 0.374981251 + -0.374981251 + x = 0.480214992 + -0.374981251 Combine like terms: 0.374981251 + -0.374981251 = 0.000000000 0.000000000 + x = 0.480214992 + -0.374981251 x = 0.480214992 + -0.374981251 Combine like terms: 0.480214992 + -0.374981251 = 0.105233741 x = 0.105233741 Simplifying x = 0.105233741Subproblem 2
x + 0.374981251 = -0.480214992 Simplifying x + 0.374981251 = -0.480214992 Reorder the terms: 0.374981251 + x = -0.480214992 Solving 0.374981251 + x = -0.480214992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.374981251' to each side of the equation. 0.374981251 + -0.374981251 + x = -0.480214992 + -0.374981251 Combine like terms: 0.374981251 + -0.374981251 = 0.000000000 0.000000000 + x = -0.480214992 + -0.374981251 x = -0.480214992 + -0.374981251 Combine like terms: -0.480214992 + -0.374981251 = -0.855196243 x = -0.855196243 Simplifying x = -0.855196243Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.105233741, -0.855196243}
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