Exercise
Factor the quadratic equation
9x^2-42x+49=0
Final Answer
Solution
9x^2-42x+49=0
It’s a quadratic equation with the coefficients:
a=9, b=-42, c=49
We solve it with the quadratic formula. Putting the coefficients in the formula gives us
x_{1,2}=\frac{42\pm \sqrt{{42}^2-4\cdot 9\cdot 49}}{2\cdot 9}=
=\frac{42\pm 0}{18}=
=\frac{14}{6}=\frac{7}{3}
We got one solution for a quadratic equation, so it appears twice in the factorizing of the equation:
9x^2-42x+49=
=9{(x-\frac{7}{3})}^2=
we can get rid of the fraction:
=3^2{(x-\frac{7}{3})}^2=
={(3(x-\frac{7}{3}))}^2=
={(3x-7)}^2
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