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Equations- Factorization of a polynomial equation – Exercise 5598

Exercise

Factor the quadratic equation

9x^2-42x+49=0

Final Answer


{(3x-7)}^2

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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