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Simplifying 7x(7x2 + -6x + 5) = 0 Reorder the terms: 7x(5 + -6x + 7x2) = 0 (5 * 7x + -6x * 7x + 7x2 * 7x) = 0 (35x + -42x2 + 49x3) = 0 Solving 35x + -42x2 + 49x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x'. 7x(5 + -6x + 7x2) = 0 Ignore the factor 7.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 '(5 + -6x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + -6x + 7x2 = 0 Solving 5 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -0.8571428571x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -0.8571428571x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + -0.7142857143 -0.8571428571x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -0.8571428571x + x2 = -0.7142857143 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 = -0.7142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -0.7142857143 + 0.1836734694 Combine like terms: -0.7142857143 + 0.1836734694 = -0.5306122449 0.1836734694 + -0.8571428571x + x2 = -0.5306122449 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = -0.5306122449 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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