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Simplifying 49x2 + -42x + 42 = 0 Reorder the terms: 42 + -42x + 49x2 = 0 Solving 42 + -42x + 49x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(6 + -6x + 7x2) = 0 Ignore the factor 7.Subproblem 1
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. The solution to this equation could not be determined.
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