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Simplifying 7x2 + -6x + -111 = 0 Reorder the terms: -111 + -6x + 7x2 = 0 Solving -111 + -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'. -15.85714286 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '15.85714286' to each side of the equation. -15.85714286 + -0.8571428571x + 15.85714286 + x2 = 0 + 15.85714286 Reorder the terms: -15.85714286 + 15.85714286 + -0.8571428571x + x2 = 0 + 15.85714286 Combine like terms: -15.85714286 + 15.85714286 = 0.00000000 0.00000000 + -0.8571428571x + x2 = 0 + 15.85714286 -0.8571428571x + x2 = 0 + 15.85714286 Combine like terms: 0 + 15.85714286 = 15.85714286 -0.8571428571x + x2 = 15.85714286 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 = 15.85714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 15.85714286 + 0.1836734694 Combine like terms: 15.85714286 + 0.1836734694 = 16.0408163294 0.1836734694 + -0.8571428571x + x2 = 16.0408163294 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 16.0408163294 Calculate the square root of the right side: 4.005098791 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 4.005098791 and -4.005098791.Subproblem 1
x + -0.4285714286 = 4.005098791 Simplifying x + -0.4285714286 = 4.005098791 Reorder the terms: -0.4285714286 + x = 4.005098791 Solving -0.4285714286 + x = 4.005098791 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 = 4.005098791 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 4.005098791 + 0.4285714286 x = 4.005098791 + 0.4285714286 Combine like terms: 4.005098791 + 0.4285714286 = 4.4336702196 x = 4.4336702196 Simplifying x = 4.4336702196Subproblem 2
x + -0.4285714286 = -4.005098791 Simplifying x + -0.4285714286 = -4.005098791 Reorder the terms: -0.4285714286 + x = -4.005098791 Solving -0.4285714286 + x = -4.005098791 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 = -4.005098791 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -4.005098791 + 0.4285714286 x = -4.005098791 + 0.4285714286 Combine like terms: -4.005098791 + 0.4285714286 = -3.5765273624 x = -3.5765273624 Simplifying x = -3.5765273624Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4336702196, -3.5765273624}
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