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Simplifying 6x2 + 131x = 2057 Reorder the terms: 131x + 6x2 = 2057 Solving 131x + 6x2 = 2057 Solving for variable 'x'. Reorder the terms: -2057 + 131x + 6x2 = 2057 + -2057 Combine like terms: 2057 + -2057 = 0 -2057 + 131x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -342.8333333 + 21.83333333x + x2 = 0 Move the constant term to the right: Add '342.8333333' to each side of the equation. -342.8333333 + 21.83333333x + 342.8333333 + x2 = 0 + 342.8333333 Reorder the terms: -342.8333333 + 342.8333333 + 21.83333333x + x2 = 0 + 342.8333333 Combine like terms: -342.8333333 + 342.8333333 = 0.0000000 0.0000000 + 21.83333333x + x2 = 0 + 342.8333333 21.83333333x + x2 = 0 + 342.8333333 Combine like terms: 0 + 342.8333333 = 342.8333333 21.83333333x + x2 = 342.8333333 The x term is 21.83333333x. Take half its coefficient (10.91666667). Square it (119.1736112) and add it to both sides. Add '119.1736112' to each side of the equation. 21.83333333x + 119.1736112 + x2 = 342.8333333 + 119.1736112 Reorder the terms: 119.1736112 + 21.83333333x + x2 = 342.8333333 + 119.1736112 Combine like terms: 342.8333333 + 119.1736112 = 462.0069445 119.1736112 + 21.83333333x + x2 = 462.0069445 Factor a perfect square on the left side: (x + 10.91666667)(x + 10.91666667) = 462.0069445 Calculate the square root of the right side: 21.494346803 Break this problem into two subproblems by setting (x + 10.91666667) equal to 21.494346803 and -21.494346803.Subproblem 1
x + 10.91666667 = 21.494346803 Simplifying x + 10.91666667 = 21.494346803 Reorder the terms: 10.91666667 + x = 21.494346803 Solving 10.91666667 + x = 21.494346803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.91666667' to each side of the equation. 10.91666667 + -10.91666667 + x = 21.494346803 + -10.91666667 Combine like terms: 10.91666667 + -10.91666667 = 0.00000000 0.00000000 + x = 21.494346803 + -10.91666667 x = 21.494346803 + -10.91666667 Combine like terms: 21.494346803 + -10.91666667 = 10.577680133 x = 10.577680133 Simplifying x = 10.577680133Subproblem 2
x + 10.91666667 = -21.494346803 Simplifying x + 10.91666667 = -21.494346803 Reorder the terms: 10.91666667 + x = -21.494346803 Solving 10.91666667 + x = -21.494346803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.91666667' to each side of the equation. 10.91666667 + -10.91666667 + x = -21.494346803 + -10.91666667 Combine like terms: 10.91666667 + -10.91666667 = 0.00000000 0.00000000 + x = -21.494346803 + -10.91666667 x = -21.494346803 + -10.91666667 Combine like terms: -21.494346803 + -10.91666667 = -32.411013473 x = -32.411013473 Simplifying x = -32.411013473Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.577680133, -32.411013473}
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