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Simplifying 11x(7x2 + 6x + 6) = 0 Reorder the terms: 11x(6 + 6x + 7x2) = 0 (6 * 11x + 6x * 11x + 7x2 * 11x) = 0 (66x + 66x2 + 77x3) = 0 Solving 66x + 66x2 + 77x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '11x'. 11x(6 + 6x + 7x2) = 0 Ignore the factor 11.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(6 + 6x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + 6x + 7x2 = 0 Solving 6 + 6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 0.8571428571x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 0.8571428571x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + -0.8571428571 0.8571428571x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 0.8571428571x + x2 = -0.8571428571 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 = -0.8571428571 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = -0.8571428571 + 0.1836734694 Combine like terms: -0.8571428571 + 0.1836734694 = -0.6734693877 0.1836734694 + 0.8571428571x + x2 = -0.6734693877 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = -0.6734693877 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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