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Simplifying 6x2 + 17x + 7 = 1 Reorder the terms: 7 + 17x + 6x2 = 1 Solving 7 + 17x + 6x2 = 1 Solving for variable 'x'. Reorder the terms: 7 + -1 + 17x + 6x2 = 1 + -1 Combine like terms: 7 + -1 = 6 6 + 17x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 6 + 17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1 + 2.833333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.833333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.833333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.833333333x + x2 = 0 + -1 2.833333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.833333333x + x2 = -1 The x term is 2.833333333x. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333x + 2.006944445 + x2 = -1 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333x + x2 = -1 + 2.006944445 Combine like terms: -1 + 2.006944445 = 1.006944445 2.006944445 + 2.833333333x + x2 = 1.006944445 Factor a perfect square on the left side: (x + 1.416666667)(x + 1.416666667) = 1.006944445 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + 1.416666667) equal to 1.003466215 and -1.003466215.Subproblem 1
x + 1.416666667 = 1.003466215 Simplifying x + 1.416666667 = 1.003466215 Reorder the terms: 1.416666667 + x = 1.003466215 Solving 1.416666667 + x = 1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 1.003466215 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 1.003466215 + -1.416666667 x = 1.003466215 + -1.416666667 Combine like terms: 1.003466215 + -1.416666667 = -0.413200452 x = -0.413200452 Simplifying x = -0.413200452Subproblem 2
x + 1.416666667 = -1.003466215 Simplifying x + 1.416666667 = -1.003466215 Reorder the terms: 1.416666667 + x = -1.003466215 Solving 1.416666667 + x = -1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -1.003466215 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -1.003466215 + -1.416666667 x = -1.003466215 + -1.416666667 Combine like terms: -1.003466215 + -1.416666667 = -2.420132882 x = -2.420132882 Simplifying x = -2.420132882Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.413200452, -2.420132882}
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