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Simplifying 7x2 + 6x + 1 = 0 Reorder the terms: 1 + 6x + 7x2 = 0 Solving 1 + 6x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.8571428571x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.8571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + -0.1428571429 0.8571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.8571428571x + x2 = -0.1428571429 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = -0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = -0.1428571429 + 0.1836734694 Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265 0.1836734694 + 0.8571428571x + x2 = 0.0408163265 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.0408163265 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.202030509 and -0.202030509.Subproblem 1
x + 0.4285714286 = 0.202030509 Simplifying x + 0.4285714286 = 0.202030509 Reorder the terms: 0.4285714286 + x = 0.202030509 Solving 0.4285714286 + x = 0.202030509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 0.202030509 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.202030509 + -0.4285714286 x = 0.202030509 + -0.4285714286 Combine like terms: 0.202030509 + -0.4285714286 = -0.2265409196 x = -0.2265409196 Simplifying x = -0.2265409196Subproblem 2
x + 0.4285714286 = -0.202030509 Simplifying x + 0.4285714286 = -0.202030509 Reorder the terms: 0.4285714286 + x = -0.202030509 Solving 0.4285714286 + x = -0.202030509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -0.202030509 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.202030509 + -0.4285714286 x = -0.202030509 + -0.4285714286 Combine like terms: -0.202030509 + -0.4285714286 = -0.6306019376 x = -0.6306019376 Simplifying x = -0.6306019376Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2265409196, -0.6306019376}
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